PDF Summaries - Catalysis, 2D metals

Inversion symmetry breaking unlocks a broad range of physical phenomena fundamental for modern technologies, motivating efforts to engineer noncentrosymmetric materials. In this context, monolayer transition metal dichalcogenides, which naturally lack inversion symmetry, have emerged as a versatile platform for valley physics, strong excitonic effects, and nonlinear optics. However, in their hexagonal stacking phase, inversion symmetry is restored in even-layer stacks and bulk form, suppressing these effects and limiting applications. In this work, inversion symmetry breaking is demonstrated in a vertically stacked tetralayer heterostructure assembled from two intrinsically centrosymmetric bilayer flakes, as evidenced by second harmonic generation measurements with an intensity comparable to that of their constituent monolayer. Spectroscopic measurements and theoretical estimations indicate that effective symmetry breaking in the tetralayer heterostructure is driven by interlayer hybridization, giving rise to pronounced electronic and phononic signatures. This symmetry breaking further induces polar anisotropy, with an intensity ratio reaching 2.36. We propose that asymmetric contributions from excitons to the second harmonic optical dipole may influence this behavior. These findings establish interlayer coupling as a critical mechanism for introducing inversion symmetry breaking and tuning the optical response of van der Waals heterostructures, providing a powerful strategy for photonics and optoelectronics in two-dimensional materials.

Defect engineering in two-dimensional materials is a powerful strategy for tuning electronic, optical, and catalytic properties. While pristine molybdenum disulfide (MoS2) has been thoroughly studied, defective MoS2 remains poorly understood due to the complexity and inconsistency of controlled defect creation. Here, we report a defect-density gradient that forms spontaneously in MoS2 flakes during chemical vapor deposition (CVD) growth. Photoluminescence and Raman spectroscopy mapping reveal the lateral arrangement of this gradient across a single flake. Deconvolution of the excitonic photoluminescence emission identifies electron doping as the key factor governing the spatial variation in optical response. This doping likely originates from sulfur vacancies formed during CVD growth, as further supported by the observed Raman mode shifts. We propose that this gradient arises from precursor depletion near the nucleation center during growth, resulting in a gradual variation in defect density. This lateral defect structure provides a convenient platform for systematically characterizing defective MoS2 across a continuous range of defect densities within a single sample. The sulfur-vacancy-driven surface activation identified here can also be important for future catalytic applications.

We investigate carrier-mediated helical magnetism in hole-doped twisted bilayer WTe$_2$ coupled to localized moments. The itinerant carriers are described by a valleyless two-flavor sliding Luttinger liquid. Via the feedback mechanism of the helical order formed within individual channels, we show that the interchannel spin susceptibility mediates a Ruderman-Kittel-Kasuya-Yosida interaction between localized moments that can stabilize a coherent helical magnetic texture across the coupled-wire array. A spin-wave analysis of the ordered state allows us to estimate the magnon energies and helix-ordering scale. The magnon energies depend on the carrier interactions with representative values falling in the microwave regime, suggesting possible detection by magnetic-resonance techniques. The helical order partially gaps the carrier spectrum and renormalizes the spin-correlation and relaxation exponents. These results identify twisted bilayer WTe$_2$ as a tunable low-dimensional platform for realizing and probing carrier-mediated helical magnetism.

Precise control of molecular heteroepitaxy offers a route to multilayer architectures with well-defined interfaces. However, the role of intramolecular flexibility in epitaxial matching remains insufficiently understood. Here, we investigate the heteroepitaxy of intact 1,3,5-tris(4-carboxyphenyl)benzene (BTB) on a molecular $\delta$-layer composed of fully deprotonated BTB molecules on Ag(111). Combining scanning tunneling microscopy, low-energy electron microscopy and diffraction, X-ray photoelectron spectroscopy, and density functional theory, we identify the key interactions controlling molecular packing and epitaxial growth. We show that intermolecular bonding motifs are preserved on the molecular template, but their lattice parameters and molecular conformations change as compared to a silver surface. Individual molecules exhibit distinct appearances in scanning tunneling microscopy, consistent with site-dependent conformational variations identified by theory. Our calculations reveal that the competition between molecule-substrate interactions and conformational energy produces different compromise geometries, resulting in conformational frustration at the epitaxial interface. Crucially, constraining BTB into a planar geometry changes the preferred lateral adsorption positions, demonstrating that molecular flexibility directly modifies the energetic preferences for epitaxial registry. Comparison with more rigid molecular overlayers further supports this interpretation. Our findings reveal that molecular flexibility contributes to epitaxial matching by allowing unfavorable molecule-substrate interactions to be compensated by energetically favorable conformations while preserving the intermolecular network.

Rydberg excitons in Cu$_2$O provide a solid-state setting for creating giant optical nonlinearities. Here, we use second-harmonic generation (SHG) to study Rydberg excitons in a doubly resonant optical microcavity designed to enhance both the pump and second-harmonic fields. We observe even-parity exciton states in an optical cavity and extend cavity-based measurements of Rydberg excitons up to $n=10$. The SHG intensity depends strongly on pump cavity detuning, showing the dominant role of the microcavity is the enhancement of the intra-cavity pump field. Analysis reveals an additional enhancement from the resonant second-harmonic cavity giving an overall SHG enhancement factor of $21 \pm 2$ inside the microcavity. These results establish cavity-enhanced SHG spectroscopy as a valuable tool for studying Rydberg excitons in microcavities and provide a pathway towards exploiting optical nonlinearities in Rydberg exciton polariton systems.

Engineering of two-dimensional material heterostructures offers a broad range of degrees of freedom through the selection of type and number of layers and their relative stacking configurations. In these compound materials, the stacking sequence plays a central role in determining electronic, mechanical, and optical properties. Here, we present a theoretical study of its signature on the excitons of hexagonal boron nitride bilayers based on first-principle calculations within the GW approximation and the Bethe-Salpeter equation. We explain how stacking-dependent symmetry variations lead to distinct electronic structures, particularly near the band edge around the K high-symmetry point, and consequently to markedly different excitonic landscapes. Indeed, we analyze the symmetry-governed character of the low-lying excitonic states, identifying their bright or dark nature for each stacking configuration and performing a systematic comparison. Our results clarify how van der Waals interlayer coupling reshapes excitons in hexagonal boron nitride bilayers and outline prospects for twist-controlled exciton engineering in this material.

Polymorphism in Mn-based chalcogenides offers access to magnetic semiconductors with distinct crystal symmetries, polar structures, and different magnetic orders. In particular, wurtzite MnSe exhibits an appealing interplay of electric polarization and several competing magnetic phases including altermagnetic order. However, stabilizing metastable polymorphs, such as wurtzite MnSe, in experimentally useful volumes remains challenging. Here, we show that a nanoscale-period MnSe/CdSe superlattice stabilizes wurtzite MnSe over micrometer-scale total thickness while suppressing the formation of the thermodynamically favored rock-salt phase. The increased magnetic volume enables bulk-sensitive characterization of this polar polymorph. The room-temperature lattice parameters of wurtzite MnSe are studied by independent experimental techniques and determined to be $a = (4.18 \pm 0.03)\,\mathring{A}$ and $c = (6.78 \pm 0.03)\, \mathring{A}$. SQUID magnetometry reveals antiferromagnetic ordering with $T_N = 62\,\text{K}$, which is accompanied by an anomaly of the MnSe lattice parameter, as oberved by temperature-dependent X-ray diffraction. Optical measurements reveal excitonic transitions pointing to the band gap at around 3.4 eV. These results highlight the utility and importance of heterostructure engineering for detailed studies of metastable phases of magnetic semiconductors, in particular wurtzite MnSe.

Advanced Functional Materials, EarlyView.

Advanced Functional Materials, EarlyView.

Superconductivity arises from Cooper pairing, but conventional photoemission probes electrons individually rather than as pairs. Here we report the observation of Cooper-pair emission from an optimally doped cuprate superconductor using two-electron angle-resolved photoemission (2e-ARPES). Below the superconducting transition, we observe a distinct two-electron emission peak at zero pair binding energy and zero pair momentum that disappears in the normal state, revealing the characteristic fingerprint of a Cooper pair. Unexpectedly, the joint energy distribution broadens markedly along the relative-energy axis as temperature decreases, while the total energy width remains nearly unchanged. This anomalous behavior cannot be explained by instrumental resolution, static disorder or thermal broadening, and instead points to scattering processes involving collective excitations of the superconductor. Our results establish 2e-ARPES as a probe of both Cooper-pair emission and the many-body dynamics of the superconducting state.

Memristors based on electrochemical metallization with many filaments are usually modeled by microscopic simulations with many parameters or by phenomenological laws whose parameters are hard to relate to physical quantities. We present an analytical mean-field model for a population of Ag filaments confined in the pores of a nanoporous matrix, built on Ohm's law, Faraday's law and a power-based rupture criterion. The filaments have a truncated normal distribution of cross-sections and rupture leaving lognormally distributed gaps whose median grows with the dissipated power. Gap closing shifts the distribution of squared gaps rigidly, and the model therefore admits closed-form expressions for the switching voltage, the read current, the rupture branch and the high-voltage current. We apply it to Ag/nanoporous anodic alumina/Al structures fabricated from industrial-grade aluminum, with a 2.4$\mu$m alumina layer, and measured under ambient conditions. The parameters were fitted to the bipolar sweeps, with the gap dispersion taken from the temporal shape of the read after a pulse. They reproduce the bipolar response, including voltage-controlled negative differential resistance, and predict without refitting the unipolar sweeps and the amplitude of the pulse response, where state memory appears. A second sample, with a larger contact deposited chemically, is described by the same model. In vacuum the devices neither switch nor show negative differential resistance, as expected if adsorbed water supplies the counter reaction; the residual high-voltage current follows ionic hopping conduction.

arXiv:2410.23544v3 Announce Type: replace-cross Abstract: Many-body ground state preparation is an important subroutine used in the simulation of physical systems. In this paper, we introduce a flexible and efficient framework for obtaining a state preparation circuit for a large class of many-body ground states. We introduce polynomial-time classical algorithms that take reduced density matrices over $\mathcal{O}(1)$-sized balls as inputs, and output a circuit that prepares the global state. We introduce algorithms applicable to (i) short-range entangled states (e.g., states prepared by shallow quantum circuits in any number of dimensions, and more generally, invertible states) and (ii) long-range entangled ground states (e.g., the toric code on a disk). Both algorithms can provably find a circuit whose depth is asymptotically optimal. Our approach uses a variant of the quantum Markov chain condition that remains robust against constant-depth circuits. The robustness of this condition makes our method applicable to a large class of states, whilst ensuring a classically tractable optimization landscape.

arXiv:1908.09304v2 Announce Type: replace-cross Abstract: The growing demand for storage, due to big data applications, cannot be met by hard disk drives. Domain wall (DW) memory devices such as racetrack memory offer an alternative route to achieve high capacity storage. In DW memory, control of domain wall positions and their motion using spin-transfer torque are important challenges. In this paper, we demonstrate controlled domain wall motion using spin-transfer torque in staggered magnetic nanowires. The devices, fabricated using electron-beam lithography, were tested using a magneto-optical Kerr microscopy and electrical transport measurements. The depinning current, pinning potential and thermal stability were found to depend on the device dimensions of the staggering nanowires. Thus, the proposed staggering configuration helps to fine-tune the properties of domain wall devices for memory applications.

High-intensity terahertz (THz) sources combining high repetition rates, strong field amplitudes, and long-term stability are key enabling technologies for next-generation ultrafast photonics. However, simultaneously achieving these characteristics in a compact and practical architecture remains a major challenge. Here, we report a high-performance tabletop THz source delivering intense single-cycle pulses at 100 kHz, generated by optical rectification in lithium niobate using an optimized echelon-based tilted-pulse-front scheme and driven by an industrial-grade ytterbium laser. The source achieves optical-to-THz conversion efficiencies exceeding 0.13% at room temperature, peak electric fields of several hundred kV/cm, and excellent long-term stability, establishing a robust platform for high-average-power strong-field THz applications. As a proof of concept, the source was integrated into an atom probe tomography (APT) instrument. APT reconstructs the three-dimensional chemical composition of materials through field-induced ion emission from a sharp nanotip. While THz-assisted ion emission has been shown to improve analytical performance by reducing thermal effects, previous demonstrations were limited to low-repetition-rate THz sources, restricting throughput and accessible analysis volumes. Using an aluminum nanotip, we demonstrate efficient THz-assisted APT at 100 kHz and benchmark its performance against conventional voltage- and laser-assisted operation. The high repetition rate enables rapid large-volume acquisition while improving mass resolving power, reducing thermal tailing, and preserving high-quality three-dimensional reconstructions. Beyond APT, this work establishes a compact and scalable high-repetition-rate THz platform for strong-field physics, nonlinear THz photonics, ultrafast spectroscopy, and material characterization at the nanoscale.

Non-volatile solutes accumulate near a receding drying front, generating concentration gradients that can drive directional colloidal transport by diffusiophoresis. This dynamic spatial arrangement of colloidal particles could affect the microstructure and macroscopic properties of the dried film. Here, we combine experiments and theory to investigate polystyrene particles suspended in electrolyte solutions drying within a capillary tube. By varying the electrolyte composition and ambient relative humidity, we show that evaporation-induced ion gradients drive particles toward the liquid-gas interface and enhance interfacial accumulation, whereas slower drying at higher humidity weakens the gradient and particle migration. We use the heat balance integral method to predict the transient solute field for a receding interface and couple it to particle transport to capture the observed particle trajectories and accumulation trends. These results identify background electrolytes and drying rate as coupled controls on particle distribution and provide a predictive framework to optimize formulation and processing parameters for manufacturing slurry-based materials, such as battery electrodes and turbine coatings.

Advanced Functional Materials, EarlyView.

Few molecular processes are more fundamental to chemistry than the autoionization of water, whose equilibrium constant, $K_w \approx 10^{-14}$, underlies acid-base equilibria and the chemistry of life. Yet the molecular origins of the free energy cost of forming and separating ions remain incompletely understood. Efforts to explain it have been limited by the difficulty of modeling water reactivity in sufficient detail. Here we combine machine learning interatomic potentials (MLIPs) with spectral adaptive biasing force enhanced sampling to connect proton transfer and water wire configurations to the underlying free energy landscape. We identify competing influences of long-range electrostatics, system size, temperature, and nuclear quantum motion on the predicted ionization thermodynamics. The free energy surface extends from neutral water to ions separated beyond the solvent-separated ion pair (SSIP). It reveals a transition state in which a proton is shared between the second and third molecules of a three-membered water wire. The contact ion pair is unstable and the SSIP only weakly metastable, so determining pK$_w$ requires sampling longer wires. Long-range electrostatics raise the free energy at ion separations beyond $3\,\mathrm{\mathring{A}}$. Models with comparable force errors give substantially different free energy profiles in this region. Increasing system size lowers the calculated pK$_w$, while nuclear quantum effects bring it closer to experiment and reproduce the higher pK$_w$ of D$_2$O relative to H$_2$O. These results establish a baseline for interpreting thermodynamic results from MLIP simulations in which charged and polar groups react and diffuse in finite cells. Our analysis also explains how cancellation among competing effects can yield ionization constants close to experiment even when simulations omit several physical contributions.

Excitons carry energy and information through a semiconductor without carrying charge. This makes them attractive for optoelectronics, but also hard to guide. Magnetic skyrmions, on the other hand, are moved by small electrical currents. Here we develop a theory of excitons interacting with a skyrmion in which the electron and the hole are treated as distinct constituents, each with its own spin--orbit coupling. We find that the topology of the skyrmion is transferred to the exciton only when the exchange coupling exceeds the relevant spin--orbit splitting. The exciton then experiences a full flux quantum, with opposite signs in the two valleys. The quantum metric of the spin texture creates a ring-shaped barrier that traps excitons, whereas the topological charge fixes the angular momentum of the trapped states and hence their optical selection rules. Because the trap moves with the skyrmion, excitons can be transported by current pulses, and small skyrmions accommodate a single exciton, which opens the door for potential hybrid applications in future information technology intertwining topological magnetic bits with optical excitations.

Site-controlled [111]-oriented quantum dots (QDs) are promising sources of non-classical light, yet their optical spectra exhibit apparently conflicting symmetry signatures. At zero magnetic field, excitonic spectra are commonly interpreted as $C_{2v}$-like, whereas measurements in Faraday geometry display selection rules characteristic of $C_{3v}$-like symmetry. Here, we show that both regimes can be described consistently without invoking any change in the underlying structural symmetry. Combining 8-band $\mathbf{k}\cdot\mathbf{p}$ theory, a self-consistent Hartree-informed configuration interaction scheme, and group theoretical analysis, we introduce a controlled symmetry reducing perturbation that lowers the QD symmetry to $C_s$. At zero field, the optical response remains predominantly $C_{2v}$-like because the additional low-symmetry transitions carry only weak oscillator strengths. In Faraday geometry, the same reduced-symmetry structure produces four dominant, nearly circularly polarised trion transitions, reproducing the experimentally observed $C_{3v}$-like response. By contrast, an exact $C_{2v}$ description inferred from the zero-field spectrum permits only two such trion transitions and therefore fails at finite field. Our results thus provide a unified description of the zero and finite magnetic field optical response without any restoration or enhancement of the underlying structural symmetry. More generally, we demonstrate that a higher-symmetry-like optical spectrum does not uniquely identify the exact symmetry of a QD, therefore also providing useful guidance for other QD and nanostructure systems that lie beyond the ones studied here.

We study nonequilibrium fluctuations of efficiency in nanostructured solar cells. Our contribution is threefold. First, we derive a microscopic stochastic model of efficiency from a two-state master equation describing absorption, radiative recombination, and extraction. This derivation establishes an explicit link between efficiency fluctuations and entropy production, and justifies the thermodynamic affinity through local detailed balance. Second, we review universal fluctuation laws established in the recent literature and apply them for the first time to the real parameters of nanostructured solar cells. We show that the total entropy production behaves as a submartingale, and that its negative exponential is a martingale. For a biased discrete random walk, the exact infimum law is verified numerically in the near-equilibrium regime, then applied to realistic solar cell configurations. Third, our simulations show that nanostructured solar cells operate in a strongly nonequilibrium regime, where negative entropy fluctuations, and hence efficiency fluctuations, are exponentially rare. Over all simulated trajectories, most configurations show no detectable negative fluctuation, consistent with the theoretical prediction. These results explain the intrinsic statistical stability of the devices and provide a conceptual and quantitative framework for understanding efficiency fluctuations around the mean values. They do not modify the mean efficiencies obtained previously, but clarify their statistical robustness in the strongly nonequilibrium regime.

Large-scale phonon calculations for structurally complex materials are limited by the cubic cost of full diagonalization. We extend the stochastic propagation method (sPM) from electronic systems to lattice dynamics for estimating phonon frequencies, constructing vibrational densities of states, and reconstructing selected phonon polarization vectors by propagating random initial vectors under the dynamical matrix. For finite-range interactions, the leading propagation cost scales linearly with atom number at fixed sampling and propagation parameters. Our error analysis shows that, for nondegenerate modes that are spectrally resolved and have nonzero frequency in the small-error regime, extending propagation yields faster asymptotic reduction of frequency-estimation errors than increasing the number of random initial states alone. Comparisons with direct diagonalization validate the spectral estimates and a selected polarization vector. Convergence tests support the predicted scaling of frequency errors for selected resolved modes.

We report the ultrafast, (sub)picosecond reduction of the antiferromagnetic order of the insulating NiO thin film in a Pt/NiO bilayer. This reduction of the antiferromagnetic order is not present in pure NiO thin films after a strong optical excitation. This ultrafast phenomenon is attributed to an ultrafast and highly efficient energy transfer from the optically excited electron system of the Pt layer into the NiO spin system. We propose that this energy transfer is mediated by a stochastic exchange scattering of hot Pt electrons at the Pt/NiO interface.

Janus transition metal dichalcogenides with broken mirror symmetry provide a novel platform for exploring many-body effects mediated by spin-valley-phonon interactions. Strong electron-phonon coupling demands a precise match between a strong effective dipole moment and nanometer-scale charge confinement. Here, we report thermally robust and enhanced trion emission in a symmetric bilayer WSeS with an S/S stacking configuration. The inward-pointing antiparallel built-in electric fields induce a strong electron confinement effect at the interface, driving dominant trion emission at cryogenic temperatures. Furthermore, a massive electron-phonon coupling strength (3.9) resonant with the optical phonon A_1^2 energy (51 meV) contributes to the thermal stability of this trion emission at elevated temperatures. By tailoring the interfacial architecture in Janus WSeS homobilayers, this study overcomes the thermal decoherence limits inherent to traditional semiconductor systems, offering novel insights into room-temperature many-body interactions.

In this work the electronic thermal conductivity of black phosphorene is studied. Using the Monte Carlo method together with the Green-Kubo relations, a statistical modelling of the motion and scattering of electrons on acoustic and optical phonons is performed to estimate the electronic thermal conductivity. The scattering probability is expressed analytically. The obtained results show a pronounced anisotropy of the thermal conductivity: the thermal conductivity values along the armchair direction are an order of magnitude larger than those along the zigzag direction, in agreement with the experimental data for related materials. In addition, the modelling allowed a more rigorous justification of some results of previous theoretical works on the anisotropic thermal conductivity of black phosphorene.

We derive a gauge-invariant clean-limit decomposition of the second-order dc nonlinear conductivity in multiband tight-binding systems within the velocity-gauge Keldysh Green's function formalism. In the constant-relaxation-time approximation, the dc response separates into four contributions with distinct lifetime $\tau$ scalings and physical origins: the nonlinear Drude term $\sigma^{\mathrm{ND}}_{ijk}\propto\tau^{2}$, the Berry-curvature-dipole term $\sigma^{\mathrm{BCD}}_{ijk}\propto\tau$, the intraband quantum-metric-dipole term $\sigma^{\mathrm{intra\text{-}QMD}}_{ijk}\propto\tau^{0}$, and the interband quantum-metric-dipole term $\sigma^{\mathrm{inter\text{-}QMD}}_{ijk}\propto\tau^{0}$. The intraband term is a Fermi-surface dipole of the ordinary band quantum metric, while the interband term is written, in the present representation, as a Fermi-sea-type response involving a band-normalized quantum metric. Working entirely within the velocity-gauge Keldysh--Kubo framework, we show that all connection-dependent commutator terms generated in the band-basis expansion cancel exactly between the covariant-quantum-connection sector $\sigma^{\mathcal{C}}_{ijk}$ and the three-Berry-connection sector $\sigma^{\mathcal{T}}_{ijk}$, making the role of the Peierls contact velocity vertices $V_{ij}$ and $V_{ijk}$ explicit; a complementary projector-based derivation appears in Ulrich et al., Phys. Rev. B 113, L201107 (2026), and our Fermi-surface dc-limit expression agrees with that reference after accounting for index and convention differences. As a diagnostic illustration, we introduce a real two-band model in which the Berry curvature and hence the BCD response vanish identically while the intraband quantum-metric dipole remains finite, establishing a practical route to quantum-metric dc responses not reducible to the Berry-curvature-dipole mechanism.

Advanced Functional Materials, EarlyView.

Machine learning from local atomic environments offers an efficient route to electronic structure, but evaluating global electronic properties in large systems remains computationally demanding. Here we combine real space charge density learning with stochastic propagation using Kohn-Sham Hamiltonians constructed from the predicted densities. The framework avoids target system self-consistent iterations and explicit diagonalization, while hierarchical blocking enables dense grid inference within limited GPU memory. We demonstrate density of states calculations for one million Si atoms and optical and transport calculations for over one hundred thousand atoms, without training separate models for each property. This framework extends the practical scale of electronic structure calculations within Kohn-Sham DFT, opening opportunities to investigate how atomic structure governs electronic, optical and transport properties at length scales relevant to real materials and devices.

How much of a neural population's measured dimensionality is the code, and how much is the act of measuring it? The slope of the participation ratio against subsample size is reported for cortical populations and for the layers of language models as a number that belongs to the system. It does not. One patch of eleven thousand mouse V1 neurons returns three slopes, 0.25 along random stimulus subsets, 0.31 along drift direction, 0.35 along neuron count, and only the middle one carries structure; the other two are the sampling floor. We split every exponent into that floor and a shift earned along a declared axis, and read the shift against two nulls: permuting the labels, and permuting them only among samples that share a nuisance. On V1 the direction-aligned shift clears the label null in eight of eight grating recordings, is positive in 32 of 32 animals in a second laboratory, and reads both sectors of the code's O(2) symmetry. The even sector sets how the ladder starts: it decides which order of adding classes climbs faster, predicts the opposite order in an equivariant network, and flows under coarse-graining by a closed-form factor that says what orientation columns do to mesoscale signals. The odd sector, carried by the direction-selective neurons, keeps the ladder climbing past half the classes. On language models the same split separates content inherited from the tokens from construction built with depth, on five architectures, and the second null shows that a grammaticality signal of twenty standard deviations is entirely carrier composition. With a floor and a declared axis, dimensionality scaling is an axis-resolved measurement, and where the axis follows a known symmetry it resolves the sector content of the code. The instrument, rung, trains no probe and reads any array or any Hugging Face model layer by layer (https://github.com/adilamin89/structure-in-the-zoom).

Magnetic ions intercalated into the van der Waals gaps of layered transition metal dichalcogenides provide a system where local moments interact strongly with a metallic host. How the order of the intercalant sublattice affects their magnetism is important but rarely addressed, although disorder is hard to avoid, in particular in thin films and heterostructures. Here this question is examined in single crystals of Ni$_x$NbS$_2$ with $0.10 \leq x \leq 0.57$, whose composition and Ni order were determined by energy-dispersive x-ray spectroscopy and synchrotron x-ray diffraction. Anisotropic magnetic susceptibility measurements reveal three regimes. Long-range antiferromagnetic order appears only for $0.25 \leq x \leq 0.33$, where the Ni ions form the $2 \times 2$ and $\sqrt{3} \times \sqrt{3}$ R$30^\circ$ superstructures, and $T_\mathrm{N}$ reaches 96 K at $x = 1/3$. In this range the effective moment, $\approx 2.5 \mu_\mathrm{B}$ per Ni, agrees with DFT+$U$ calculations, in which the Ni spin is partly delocalized onto the surrounding S ligands. For $x \leq 0.18$ the dilute, randomly distributed Ni ions remain paramagnetic down to 2 K with a reduced moment. For $x \geq 0.37$, where Ni-Ni contacts are unavoidable, long-range order gives way to a short-range ordered state below 10-15 K with a further reduced moment. As calculations for ordered Ni arrangements find the Ni state nearly independent of $x$, even at $x = 1/2$, the reduction of the moment is attributed to a disorder-enabled reduction of the charge transfer from Ni to the NbS$_2$ layers. The magnetism of Ni$_x$NbS$_2$ is thus governed by the (dis)order of the Ni sublattice rather than by the Ni concentration alone.

We extend the scalability of variational infinite two-dimensional tensor network methods with application to investigate frustrated magnetism of the square-lattice $J_1$-$J_2$ model and kagome-lattice Heisenberg model. In the sign-problem-free limit of the square-lattice model, we achieve high ground-state energy precision comparable to quantum Monte Carlo methods. With no obstruction beyond this limit, our method obtains direct estimates of order parameters. For the square-lattice $J_1$-$J_2$ model, we determine isotropic plaquette order in the valence-bond solid region. For the model near $J_2/J_1=0.5$, and the kagome lattice Heisenberg model, our data indicate linear-dispersion gapless states. To probe the candidate spin-liquid nature of the highly frustrated cases, we go beyond inferring the absence of symmetry-breaking orders and analyze susceptibilities that characterize gapless spin liquids. By estimating scaling dimensions, our data indicate a stable gapless spin liquid on the kagome lattice, and competing scenarios for the intermediate regime of the square-lattice model. Our developments include parallelization and randomized low-rank methods and largely expand the frontier of high-precision variational numerics for quantum phases of matter.

We demonstrate sequential single-atom-resolved imaging of the same ultracold atomic sample and apply this technique to quantum-walk measurements in an optical lattice. In quantum gas microscope experiments, fluorescence imaging provides microscopic information on atomic distributions but induces motional heating through photon scattering, making it difficult to reuse the same sample for subsequent quantum dynamics. To overcome this limitation, we apply Raman sideband cooling with parameters optimized for post-imaging cooling, enabling sequential single-atom-resolved measurements of the same sample. By optimizing the cooling parameters with machine learning, we achieve high fidelity over multiple imaging cycles. To demonstrate the capability of this technique, we measure one-dimensional quantum walks of single atoms in an optical lattice. By determining the initial atomic positions from fluorescence images, we extract quantum-walk transition probabilities without requiring deterministic preparation of the initial atomic positions. The observed dynamics agree with numerical simulations of quantum walks of single atoms. Our method provides a route toward reducing experimental overhead in quantum gas microscope studies requiring repeated acquisition of spatially resolved correlation data.

We present an implementation of the bare and interacting longitudinal susceptibility in a full-potential linear muffin-tin orbital code. The bare susceptibility is built in real space from Matsubara sums of Kohn-Sham Green's functions and is resolved by site, spin and orbital degrees of freedom; the spin and charge susceptibilities follow from a Dyson equation, with an on-site exchange-correlation kernel. After testing the solver on the Stoner-like instability of bcc Fe, we apply it to four density-wave materials. The bare susceptibility peaks at H in bcc Cr, where the nonmagnetic state is close to a Stoner instability, and at the stripe vector M in FeSe. In LaTe3 the response of the Te nets peaks close to the observed charge-density-wave vector, at its image in the neighbouring Brillouin zone; which of the two equivalent vectors carries the response is set by the phases of the sites in the cell. In 2H-NbSe2 the response is weakly modulated, and the observed vector lies on the flank of a broad maximum, consistent with the known importance of electron-phonon coupling there. Antiferromagnetic order reduces the bare longitudinal response at the ordering vector by ~8% in Cr and about half in FeSe. The orbital decomposition of the bare susceptibility shows which orbitals contribute the most for the nearest-neighbor bonds.

arXiv:2605.18187v3 Announce Type: replace-cross Abstract: We develop a microscopic theory of quantum-particle propagation through quasi-static electrostatic fluctuations of a classical one-component plasma. The RPA potential is Gaussian but has an unscreened $1/r$ correlation tail, which makes the disorder-averaged retarded Green function infrared sensitive. Its eikonal attenuation scale is $\ell_{\rm w}=k^2/G$ for $g=G/k^3\ll1$, with the formal strong-saddle asymptote $\ell_{\rm s}=(4\sqrt[3]{2}/3)G^{-1/3}$ for $g\gg1$. For a slab of thickness $d$, the retarded--advanced mutual-coherence kernel is infrared finite: the coherence decays algebraically for $\lambda_D\ll\rho\ll d$ and saturates at larger transverse separation. Thus equilibrium ionic-density fluctuations constitute a distinct quasi-static dephasing channel with a nonexponential coherence law. A finite coherence radius exists only when the saturation threshold is crossed. Relativistic paraxial reduction gives $a_{\rm rel}=1/(\hbar v)$ and the finite high-energy limit $1/(\hbar c)$. The ionic contribution is very small at conventional TEM energies for a $100\,\mathrm{nm}$ water-like layer. Within the quasi-static model it grows for thicker samples and lower-energy electrons, while sub-keV transmission through liquid water is strongly limited by inelastic scattering.

The anyon-Hubbard model is the paradigmatic lattice model of one-dimensional (1D) anyons, in which chiral interactions make bosons equivalent to particles with fractional statistics. Its continuum limit, the chiral BF theory, emerges as the low-energy description of a Raman-coupled Bose gas with imbalanced interactions. Here, we show that loading such a gas into a 1D optical lattice realizes the lattice counterpart of this theory, which we name the Raman anyon-Hubbard model. The Raman-dressed bosons acquire density-dependent Peierls phases when tunneling through occupied sites. For a small statistical phase, the model reduces to the anyon-Hubbard model, while beyond this limit it defines a distinct lattice anyon model with unbounded rather than periodic statistical interactions. Numerically, we show that the dressed gas displays the defining properties of 1D anyons, namely a density-dependent asymmetry of the ground-state momentum distribution, interaction-induced asymmetric transport and chiral bound states. Remarkably, these features are readily accessible with Raman-coupled $^{39}$K atoms, opening up the experimental exploration of 1D anyons beyond the few-particle regime.

Free fermions exhibit Eigenstate Typicality (ET) meaning that the reduced density matrix, $\rho$, of a small spatial subsystem of a {\sl single}, typical, excited energy eigenstate is gaussian with a modular hamiltonian, $h \equiv -\log \rho$, asymptotically proportional to the free fermion hamiltonian. In effect, the ET may be thought of as providing an independent route to establishing the Fermi-Dirac (FD) distribution for free fermions. We revisit this argument for fermions belonging to a superposition of degenerate eigenstates. Specifically, we show that the modular hamiltonian corresponding to a superposition of degenerate eigenstates in a 1-d free fermion lattice system is interacting, and therefore the reduced density matrix for the subsystem is not gaussian. Measurements of the single particle distribution of a small subsystem would then exhibit non-thermal deviations from the FD distribution. These features may be traced to a violation of Wick's theorem for the chosen excited state. We develop a perturbation theory for the modular hamiltonian corresponding to a weak mixture of degenerate states and study the modular hamiltonian (exactly) computationally. Finally, we speculate that initial conditions in a realistic fermi system evolving towards equilibrium might be encoded in the interaction terms of the modular hamiltonian and consequent correlations of fermions.

High throughput computational databases such as Materials Project, the Open Quantum Materials Database, and Alexandria now each list on the order of 10^5 predicted stable compounds. However, the overall reliability of these predictions in terms of actual experimental synthesizability remains poorly understood. In this work we attempt to synthesize, via arc melting, 34 different predicted ternary compounds. The majority of these materials did not form in the predicted structure, instead resulting in disordered variants or multiphase mixtures. Four formed ordered structures not reported before, one of them at a composition reported earlier without a structure. We discuss both the failures and the successes, and identify simple filtering criteria that can help researchers avoid hypothetical materials that are unlikely to form.

We study the effects of Coulomb screening on the second-order dc response in finite-size diffusive conductors. Starting from the Boltzmann equation supplemented by the self-consistent electrostatic field, we develop a kinetic theory of the inverse Faraday effect for a two-dimensional disk driven by a circularly polarized ac electric field. In this formulation, the first-order charge modulation and the induced electric field are coupled through the Coulomb interaction, and the self-consistent first-order solution determines the nonlinear source for the second-order dc circulating current responsible for the induced magnetic moment. The radial problem is solved numerically using an angular-harmonic expansion and the Chebyshev collocation method. It is shown that in the non-self-consistent approximation the frequency dependence of the second-order dc response has a maximum when the diffusion length associated with the radiation frequency becomes comparable to the sample radius. This behavior is found to be strongly modified by self-consistent screening. We demonstrate that Coulomb screening shifts the maximum of the dc response to a higher drive frequency and suppresses the peak amplitude. This behavior is observed consistently for the area-integrated circulating current and the induced magnetic moment. The obtained results clarify the limitations of the non-self-consistent description of the inverse Faraday effect and show that Coulomb self-consistency is crucial for quantitative predictions of optically induced dc magnetization in finite-size diffusive conductors.

In this contribution, we review existing multivalent models of Influenza A Virus (IAV) systems to study virion dynamics and design of multivalent entry blockers. We review existing biochemical estimations of the dissociation constants and catalytic activities of the two virion ligands [hemagglutinin (HA) and neuraminidase (NA)], which can be used to develop quantitative theories and experiments. Multivalent models are statistical mechanics frameworks for studying the simultaneous interaction of multiple reversible ligand-receptor bonds. They quantify the effects of both combinatorial entropy terms and single-molecule ligand-receptor affinities. Multivalent frameworks led to the rationale of superselectivity, the ability of probes to sense specific concentrations of conjugated receptors. Multivalent models guided the design of antiviral nanomedicines constituted by polymeric scaffolds conjugated with small molecules such as sialic acid receptors targeting the ligands on the surface of the virion. Importantly, neuraminidase is an enzyme that limits the number of host-guest bonds through receptor desialylation. Like active particles, neuraminidase activity enhances virion motility in the extracellular medium. Modeling the dynamics of Influenza A virions requires developing out-of-equilibrium multivalent models.

Materials underpin modern technologies, from energy harvesting, storage, and conversion to information and communication technologies. Their functionality is often governed by the interplay between competing phases, and thermodynamic behavior shapes microscopic properties and ultimately determines technological performance; for instance, the light absorption of inorganic metal-halide perovskites in solar cells. Accurately predicting crystal thermodynamics, however, remains a major challenge for computational approaches because strong anharmonic effects require extensive sampling of the potential energy surface. Here, we present an on-the-fly Bayesian framework, combined with the stochastic self-consistent harmonic approximation, for learning first-principles potentials. This approach enables the prediction of thermodynamic properties over a broad temperature range with first-principles accuracy while requiring training on only a few atomic configurations. A relevant finding is that the majority of the required structures are obtained from a single inexpensive dataset generation step, demonstrating that the relevant physics for accurately predicting solid-state thermodynamics is encoded in a few physically meaningful configurations. We investigate the thermodynamic and dynamical properties of Li$_2$O, $\alpha$--CsPbI$_3$, and $\delta$--CsPbI$_3$, requiring only 44, 256, and 50 total-energy calculations, respectively. Notably, we show that this framework accurately captures the extreme thermal expansion of \ce{Li2O}, and the phase diagram of CsPbI$_3$ with a predicted transition temperature within 20 K of experiment. More broadly, the method presented opens an interesting route toward accelerated materials engineering under realistic conditions for a wide range of technologically relevant applications, including batteries, photovoltaics, and memristors.

Light can control magnetic order on ultrafast timescales, but for a two-dimensional magnet with an out-of-plane order parameter $\boldsymbol N\parallel\hat z$, the inverse Faraday field is collinear with $\boldsymbol N$ and gives no transverse torque. Here we show that bichromatic $(\omega,b\omega)$ light generates electronic torques perpendicular to $\boldsymbol N$ in Rashba-coupled magnetic multipoles, from $p$-wave ($n=1$) magnets to $i$-wave ($n=6$) altermagnets. Beyond high-frequency effective fields, we evaluate the exact Floquet response and the generalized torque per occupied electron, for prescribed occupations. The momentum-dependent exchange terms dominate this Fermi-sea torque and remove the leading-order zeros (amplitude-ratio blindspots) of the momentum-independent field in the channels tested. For out-of-plane $\boldsymbol N$, rotational symmetry permits a transverse torque only if $\gcd(n,b+1)=1$ for counter-rotating beams or $\gcd(n,b-1)=1$ for co-rotating beams. For in-plane $\boldsymbol N$, the Fermi sea also gives a torque component along $\hat z$ that the momentum-independent field cannot produce. We classify the active channels, with $n=1,\dots,6$ and $b=1,\dots,7$, by frequency scaling and origin (cycle-averaged versus oscillating exchange). As a control, a Rashba ferromagnet ($n=0$) has one symmetry-allowed out-of-plane channel and a weak in-plane response without a selection rule. Finite-momentum occupied-state physics is therefore essential for light-driven torques in unconventional magnets, and the exact Floquet calculation validates and extends the high-frequency description.

The recent success of foundation models and deep learning has far outpaced our theoretical understanding of how large-scale neural networks learn and generalize. Statistical physics provides a natural language for describing such high-dimensional, nonlinear, and strongly coupled systems, offering concepts such as mean-field theory, phase transitions, energy landscapes, and stochastic dynamics. In this topical review, we adopt a statistical-physics way of thinking -- from concepts including phases and criticality, and free-energy viewpoints, to methods such as kernel and Gaussian-process limits, mean-field and dynamical mean-field theories, random-matrix tools, and Fokker-Planck formalisms, and to a mindset emphasizing universality, scaling, and tractable limits with explicit validity regimes. We survey recent progress on understanding modern deep learning through this lens, including mean-field analyses of wide networks, spectral and geometric perspectives on loss landscapes, stochastic-gradient-based training viewed as a dynamical process, and phase-transition analogies that organize phenomena such as overparameterization, generalization, and representation change. Our goal is to synthesize these threads into a coherent framework that clarifies what each approximation explains, when it is expected to hold, and how apparently competing narratives relate or diverge. Together, these perspectives form a unified physical framework that views representation learning as a collective phenomenon in high-dimensional systems, bridging deterministic and stochastic regimes of gradient-based optimization.

We study the unitary Fermi gas in an external trap in the double-scaling limit of large flavor number N and large charge Q at fixed Q/N. At leading order, the problem reduces to the spectral zeta function of a BdG operator in an inhomogeneous pairing background. The grand potential admits a gradient expansion with distinct bulk and edge sectors. We show that when the trap is harmonic, the bulk sector expansion terminates: beyond the first three terms every bulk contribution integrates to zero. This cancellation is general and follows from zeros of the Euler beta function computed in the Son-Wingate effective field theory, independent of the low-energy constants. The truncation persists for anisotropic traps in any odd dimension. All higher-order dependence for harmonic potentials is therefore carried by the droplet edge. For anharmonic traps, the asymptotic bulk series is factorially divergent. Using a heat-kernel WKB analysis, we show that its large-order growth, sign oscillations, and optimal truncation are fixed by complex periodic orbits of the BdG problem, which are analytic continuations of Andreev reflections. We numerically confirm the predicted Borel singularities for quartic and sextic traps.

Designing a crystal for a target property requires choosing its elements, stoichiometry, and atomic structure together, yet gradients exist only for the continuous structural variables. We introduce differentiable Equiformer fast effective-atom theory (DEFEAT), which lets a pretrained EquiformerV3 foundation model accept continuous species weights and site occupancies without retraining on fractional data, thereby enabling gradient-based materials optimization. Gradients from fine-tuned property models and a machine-learned energy penalty then guide updates to composition, atom count, atomic positions, and lattice vectors in a single optimization. In a search for phonon-mediated superconductors, density-functional perturbation theory on 45 structurally novel designs gives isotropic Allen-Dynes critical temperatures above 10 K for 39; the highest is 24.0 K for ZrTiNb2CN3, and H4LiPd3 (23.2 K) lies on the static DFT hull. In searches for photovoltaic absorbers, SCAN calculations confirm ten novel crystal structures with band gaps within 20% of a 1.34 eV target on their respective raw or empirically corrected scales, all within 70 meV/atom of the DFT hull, and show that the systematic gap error of the training functional propagates into the designs unless the objective corrects for it. Quasiharmonic free energies from machine-learned potentials further show that finite-temperature competition with solid phases can reorder candidates relative to the static hull.

arXiv:2512.06762v3 Announce Type: replace-cross Abstract: The critical phenomena of 2D antiferromagnetic $Q$-state Potts model on the square lattice with $Q=2,3,4,5$ and 6 are investigated using supervised neural networks (NN). Conventional supervised and unsupervised NNs either fail or have difficulty in identifying the correct critical behaviors of these models. Remarkably, despite the fact that the NNs employed here are trained with a particular fixed type training set which contains no information about the considered models (except for $Q=2$), they correctly compute the critical temperatures for the studied physical systems. Particularly, the NN outcomes suggest convincingly that the $Q=3$ model is critical only at zero temperature and $Q=4,5,6$ models remain disordered at all temperatures. Apart from the studied models, our NNs trained with exactly the same training set have successfully determined the critical temperature(s) and the nature of the associated phase transition(s) of another physical system differing dramatically from those considered here. Therefore, our NN has the potential to be a universally applicable NN model in studying phase transitions.

Conventional thermal emitters obey Kirchhoff's law of thermal radiation, which requires emissivity and absorptivity to be equal at each wavelength, angle, and polarization. This in turn places a fundamental limit on a range of radiative energy technologies as well as heat transfer. This constraint can however be overcome using magneto-optic semiconductors, which break Lorentz reciprocity under an applied magnetic field. However, in most prior experimental demonstrations, nonreciprocity has been restricted to TM polarization, since the electric field of TE-polarized light is parallel to the applied magnetic field. Here, we experimentally demonstrate nonreciprocal absorption in both polarizations at the same wavelengths and angles from a single structure, wherein a germanium Mie-resonant metasurface on a doped InAs layer scatters TE-polarized light into near fields with components perpendicular to the magnetic field, allowing the magneto-optic response of the InAs to act on them. Under a 0.48 T field from a permanent Halbach array, this structure exhibits a difference in absorptivity between $+B$ and $-B$ of 0.035 in both TE and TM polarization at 16.6 $\mu$m. Our approach shows that the magneto-optic response of a planar semiconductor and the resonances of a dielectric metasurface can be designed together, offering a potential route to dual-polarization nonreciprocity at fields available from permanent magnets for emerging energy and heat transfer technologies.

We investigate the spectroscopic response of a repulsively interacting, infinitely heavy impurity moving at constant velocity $v$ through a one-dimensional ideal Fermi gas. Using an exact functional-determinant approach, we calculate the Ramsey response and spectral function, fully accounting for many-body particle-hole excitations. We uncover a strongly nonmonotonic dependence on impurity velocity: decoherence is enhanced around the Fermi velocity, whereas sufficiently rapid motion restores a narrow, long-lived polaron resonance. A long-time wave-packet analysis yields analytical expressions for the polaron energy and decay rate over the full velocity range and quantitatively captures the numerical results. At high velocity, the polaron energy approaches the mean-field value, the decay rate vanishes as $1/v$, and the spectral weight approaches unity. Thus, rapid prescribed motion provides a dynamical route to suppressing the orthogonality catastrophe and restoring polaron coherence even for an infinitely heavy impurity, where recoil is entirely absent.

All-dielectric metasurfaces supporting quasi-bound states in the continuum (qBICs) have emerged as powerful platforms for biosensing, yet their operation remains largely concentrated in the visible and near-infrared regimes. Extending these resonances into the deep-ultraviolet (DUV) to probe the intrinsic electronic absorption of biomolecules presents substantial material and nanofabrication challenges. Here, we experimentally demonstrate a hafnium dioxide (HfO$_{2}$) metasurface supporting DUV qBICs in the wavelength range from 225 nm to 340 nm with quality factors reaching 500. We further demonstrate its refractive index sensing capabilities through integration with a microfluidic cell and optical characterization in reflection mode. We show that the introduction of an aqueous buffer leads to a further quality factor enhancement. Achieving a sensitivity of up to approximately 60 nm/RIU and an operational figure of merit of 40 $\mathrm{RIU}^{-1}$, this low-loss HfO$_{2}$ metasurface provides a robust foundation for label-free DUV biosensing.

Collisionless self-gravitating systems, such as merging galaxies, have long seemed an exception to the statistical-mechanical principle that chaotic many-body systems relax to maximum-entropy states: Lynden-Bell's statistical mechanics of their "violent relaxation," constrained by exact conservation of phase-space volume -- equivalently, of infinitely many collisionless "Casimir" invariants -- has appeared not to be a good description. We propose that violent relaxation does give rise to Lynden-Bell's maximum-entropy equilibria, but that both are underpinned by gravitational turbulence, in which large-scale gravitational fluctuations drive chaotic phase-space mixing of the particles' distribution function. We derive the universal small-scale (sub-Jeans) spectra of this turbulence and show that it leads to phase-space-volume conservation being broken on a timescale only logarithmically longer, in the particle number N, than the dynamical (violent-relaxation) time. This timescale separation lets the system relax "adiabatically" through a sequence of Lynden-Bell equilibria, each corresponding to instantaneous values of the Casimirs. At long times, it approaches an equilibrium close to its "ground state": a distribution whose Casimirs have adjusted so that the system's energy is now its minimum possible energy. Thus, the system's universal tendency is toward a minimum-energy, maximum-entropy state. We corroborate this picture with 1D N-body simulations and hypothesize that it can explain the universal equilibria of galaxies and dark-matter halos.

Proposals for nonreciprocal quantum batteries identify the point of complete nonreciprocity, where coherent and reservoir-mediated couplings balance, as the operating point for enhanced charging. We show that, for batteries built from interacting qubits, this point is, in general, suboptimal. The optimal design is set by a more intricate interplay between the coherent coupling and the local and collective dissipation rates, of which complete nonreciprocity is only a special case. We consider a many-body battery charged by a driven many-body charger, with each qubit coupled to a local bath and the complete setup immersed in a shared engineered reservoir. For a weakly driven two-qubit setup, we prove the Dzyaloshinskii-Moriya interaction to be the optimal coupling, and show that the battery capacity is maximized at a coupling strength fixed by the local and collective dissipation rates, which coincides with complete nonreciprocity only for a specific balance between them. The shared reservoir enhances the capacity for couplings weaker or stronger than both local dissipation rates, and can increase the extractable work even where it reduces the capacity. At strong drive, with the Dzyaloshinskii-Moriya interaction between the charger and the battery, the capacity is bounded by $1/2$. For qubits arranged in a star network with a single central battery qubit, these results remain qualitatively unchanged, while the maximum capacity of a battery charged by $N_A$ weakly driven charger qubits saturates with $N_A$ in the presence of the shared reservoir, approaching its limit as $N_A^{-1}$. In contrast, the maximum capacity of $N_B$ qubit batteries charged by a single-qubit charger decays as $N_B^{-2}$.

The performance of thermal machines is characterized with several, often competing quantities, such as power, efficiency, energy waste, and resilience to environmental noise. We employ multi-objective optimization to find the best thermal machines operating in the irreversible linear-response regime. We derive exact analytical parameterizations for the optimal (Pareto) fronts associated with mean extracted power, efficiency, entropy production and the amplitude of power fluctuations. These optimal fronts set the quantitative fundamental limits for the performance of linear-response machines, which are achieved under tight coupling conditions (endoreversible machines). The geometry of the fronts is universal: two-, three-, and four-objective trade-offs follow analytical formulae that do not depend on the value of any physical parameter of the machine. Furthermore, we test our results with existing experimental data from different physical systems operating also beyond the linear regime, ranging from atomic to macroscopic scales, and including single-atom engines, colloidal systems, macroscopic engines and power plants.

Exceptional points (EPs) are a hallmark of non-Hermitian physics, giving rise to extreme sensitivity and enhanced dynamic response. Such unique spectral singularities have been extensively studied in classical photonics, both at theoretical and experimental levels, where the relevant observables are evident. That is not necessarily the case in the quantum regime, where this kind of behavior around EPs, to a large extent, remains elusive. In fact, the interplay between dissipation and quantum fluctuations makes the complete Lindbladian evolution quite different from effective non-Hermitian Hamiltonian descriptions. In this context, we investigate the signatures of the Liouvillian EPs on spectral and dynamic response by considering properly normalized long-time averages and imbalances. Even though our approach is generic, we focus on two paradigmatic models-a lossy Bose-Hubbard lattice and a dissipative two-spin system, where we investigate the role of quantum jumps and interactions in the Liouvillian spectrum, in terms of complex and structured pseudospectra. Our results demonstrate how non-Hermitian phenomena emerge in realistic quantum lattices, providing a bridge between classical EP physics and experimentally accessible open quantum systems.

Quantum thermodynamics seeks to characterize possible state transformations under thermodynamic constraints in microscopic quantum systems. In the fully quantum regime, however, quantum coherence imposes various restrictions on state conversions, and a complete characterization of state convertibility has remained open. Here we resolve this problem for asymptotic conversions between pure states. Specifically, we show that asymptotic convertibility is fully determined by the free-energy and energy-variance ratios. Our result reveals how genuinely quantum effects quantitatively constrain state conversions in quantum thermodynamics.

Perfect wave transfer (PWT) reproduces spatial reflection at a common finite time under a fixed Hamiltonian. We classify this process for open compact bosons and inhomogeneous Tomonaga--Luttinger liquids, distinguishing transfer of oscillator and neutral observables from transfer on the charged field algebra. In the single-charge model, the first two notions coincide. Global transfer additionally requires rephasing of the compact zero mode. For regular reflection-symmetric channels, exact oscillator transfer forces an odd multiple of the optical crossing time and a strictly ordered, parity-compatible spectrum differing from the conformal ladder at only finitely many levels. This spectral condition is also sufficient when the Robin boundary data induced by the physical profile are included. Requiring Neumann conditions after the Liouville transformation instead forces conformality. We construct an explicit, regular one-defect family for every $r1/2$. Its transfer parameters are precisely the reduced fractions $r=p/q$ with odd numerator and denominator, with shortest transfer time $pL/v_0$. At the delay $3L/v_0$, the $r=3/5$ profile has numerical contrast $K_{\max}/K_{\min}\simeq 12.913$, compared with $81$ for $r=3$. Two independent conservative discretizations show second-order convergence on fixed mode bands. Occupation- and charge-constrained error estimates quantify robustness, while an exact homogeneous-chain calculation explains the $J^{2/3}$ resolved-band scale also observed in the engineered channels. These results provide a spectral design method and finite-device benchmarks for quadratic quantum channels. An interacting microscopic realization remains open.

Gravity is by far the weakest among all known interactions. While it dominates the large-scale structure of the universe, gravitational interactions between small masses in the microscopic range remain underexplored because they are too weak to be experimentally accessible. The interface between gravity, described by general relativity, and quantum mechanics, which describes the microscopic world, is of particular interest. From a theory standpoint, these two major descriptions of nature have not been combined in a satisfactory manner. Technology is gradually becoming mature enough such that probing gravity at the microscopic scale, where quantum mechanics and gravity potentially meet, is becoming accessible. Explorations towards genuine quantum gravity have to be carried out under conditions where the gravitating masses possess non-classical properties, which necessitates ultimate protection against disturbances, such as ultralow temperatures and a small range of motion. Here, we present an experiment at millikelvin temperatures, where the gravity due to a micron-range coherent displacement of an 87 mg source mass imprints on the motion of an oscillating membrane loaded with a 1.3 mg test mass. Vibrations of the membrane are measured in the microwave optomechanical scheme, which is a key setup for investigating non-classical motional states of mechanical oscillators. When considering the combination of total source and test masses, our setup presents two orders of magnitude progress in sensing gravity at the small scale, as well as a 35 dB improvement of gravitational sensitivity at kHz frequencies or above. Our setup offers a plausible approach for studying gravitational interactions between masses prepared in non-classical motional states.

In this work we study the discrete Smoluchowski equation with a multiplicative kernel and an additional term describing the spontaneous shattering of each particle into monomers at a constant rate $\lambda$. We show that the introduction of fragmentation suppresses gelation for $\lambda \ge 4$. We derive analytical expressions for the second moment and the monomer concentration $n_1(t)$. These expressions lead to a recurrence relation allowing the steady-state particle size distribution for $\lambda \ge 4$ to be calculated with machine precision. We validate our analytical and semi-analytical results via numerical simulations using a solver that employs the Fast Fourier Transform for computation of the right-hand side and a second-order Runge-Kutta method with adaptive time steps.

Standard uncertainty quantification methods for machine learning interatomic potentials often fail to quantify the effects of model misspecification despite its prominence as a source of error. To combat this, misspecification-aware uncertainty schemes have been gaining attention, pointwise optimal parameter set regression (POPS-Regression) among them. However, no guarantees on the physicality of the posterior distribution are given and uncertainty estimates can be conservative compared to the true error. To combat this, we present a model misspecification aware scheme that builds on POPS-Regression by allowing users to specify physical priors that are enforced across the obtained ensemble of models. This allows the user to incorporate misspecification-aware uncertainties without compromising on physical properties. The scheme is applicable to any physical quantity that can be represented by a convex set of parameters and so is robust for a wide variety of static properties which can help inform dynamical simulations. Here, we demonstrate the scheme for phononic vibrations and elastic properties. The scheme is also applied to both linear and message-passing neural network potentials by exploiting the linearity available in both architectures; for neural network potentials we approximate the readout layer as a linear model based on fixed non-linear features. The versatility of the method provides an alternative to hand-crafted or active learning approaches to data-set construction to correct physical failures by adding data thus reducing the computational overhead for designing potentials for specific applications.

We present here a numerical study of the Toda lattice Hamiltonian dynamics showing how, despite model integrability, it is possible to find many macroscopic observables which display standard equilibrium behavior. In particular, we study numerically the energy time correlation of certain coarse-grained variables, showing that it decays with either exponential or stretched exponential behaviour, thus indicating good thermalization properties. The spirit of our observation is complementary to that of standard Fermi-Pasta-Ulam-Tsingou-like numerical experiments, in which the breaking of integrability is regarded as the key ingredient for relaxation to thermal equilibrium. The present communication corroborates, on the contrary, the view that integrability is not an obstacle to thermalization, provided that a sufficiently weak definition of the latter is accepted. In the Toda lattice we have introduced several kinds of coarse-grained variables, constructed with the purpose to maintain a thermodynamic relevance also for large system sizes, which all show good thermalization properties.

The evolution of electron correlation in the superconducting state of the mixed-crystal series $\lambda$-(BETS)$_2$GaBr$_x$Cl$_{4-x}$ was investigated by magnetic and transport measurements. Br concentrations evaluated by electron-probe microanalysis agree well with single-crystal X-ray diffraction refinement. Demagnetization-corrected susceptibility and magnetization of crystals with $x_{c(rf)}$ = 0.22, 0.24, 0.42, and 0.63 all show a diamagnetic superconducting transition. The lower critical field $H_{c1}$, determined from the deviation from the Meissner response, shows a dome-like maximum at $x_{c(rf)}$ = 0.24. The upper critical field $H_{c2}$, obtained from the first high-field magnetoresistance measurements in this system, decreases with increasing Br concentration up to $x_{c(rf)}$ = 0.42, establishing the high-field superconducting boundary on the chemical-pressure side. Combining these results with reported transport data under chemical and physical pressure, we propose a pressure-temperature phase diagram for $\lambda$-(BETS)$_2$GaCl$_4$. Its double-dome-like structure has a local minimum near x = 0, where a quantum-critical point was proposed at P $\approx$ 0.13 GPa, separating a low-pressure regime of superconductivity coexisting with magnetism and an unconventional metallic state from a higher-pressure regime with conventional metallic behavior. A low-temperature resistivity upturn, previously reported only under physical pressure, is also found under chemical pressure, suggesting that spin-density-wave fluctuations may extend continuously across both pressure axes. The phase diagram overlaps with that of $\lambda$-(STF)$_2$GaCl$_4$ under physical pressure, indicating that chemical substitution, external pressure, and molecular substitution can be unified in a single bandwidth-controlled phase diagram for $\lambda$-type molecular superconductors.

Machine-learned interatomic potentials are misspecified, so Bayesian posterior variances understate their errors. For linear atomic cluster expansion (ACE) potentials we derive calibrated uncertainties from one misspecification-robust parameter covariance, the delete-one-configuration jackknife. Scaled by one conformal quantile from a held-out part of the training set, it gives per-atom force uncertainties close to their target coverage on held-out silicon data and on cracks left out of the fit; screw dislocations left out are under-covered by the smaller of the two models. With one scale fitted to the forces of a held-out test split, the same parameter distribution is propagated to 21 properties of silicon, from elastic constants to defect and surface energies, by implicit differentiation through each relaxation and by committees, and is tested against density functional theory (DFT) without tuning on any property. For a smaller and a larger model the intervals cover most properties, and the larger model's are about 4 times tighter. The Bayesian posterior with one calibrated scale has the wrong shape: it covers fewer properties and has far lower joint evidence. Pointwise optimal parameter sets (POPS), once their hypercube is numerically defined, performs comparably on the properties, but its per-atom force regions are not calibrated to a target (0.95 and 0.84 at a nominal 0.90). Where the jackknife fails is relaxed point defects, whose training cells are all hot snapshots: a bias that every configuration shares is invisible to a jackknife, but it can be measured from the training labels, and as a discrepancy term, devised after the property results were seen, it brings the coverage close to nominal.

Krylov subspace methods efficiently approximate extremal eigenstates and eigenvalues of many-body Hamiltonians, but non-orthogonal bases can suffer from ill-conditioning. This challenge is amplified in quantum computing, where direct state access and thus straightforward orthogonalization are unavailable. We investigate a variational Krylov-like framework that iteratively optimizes a parametrized sequence of states to mimic Lanczos-like couplings while penalizing linear dependencies. Analyzed against exact Krylov and Lanczos on a finite Anderson impurity model, ansatz expressivity strongly influences the performance: Hamiltonian-inspired ans\"atze preserve Krylov-like convergence while improving the conditioning, whereas shallow ans\"atze remain stable but miss low-energy directions.

We study the covariant higher-rank Chern-Simons theory of fractons in 2+1 dimensions in the presence of a planar boundary. The differential generator associated with the scalar gauge symmetry singles out a single scalar Ward combination of the functional field equations. Its zeroth and first normal moments give two integrated boundary identities. The zeroth moment yields a traceless rank-two current obeying a fractonic double-divergence conservation law and a higher-rank Kac-Moody algebra. The first moment makes the normal-tangential field $w_i=h_{2i}$ explicit and yields an ordinarily conserved vector current with a standard $U(1)$ Kac-Moody algebra. Functional differentiation also produces a mixed equal-time bulk-boundary commutator between $w_1$ and $h_{11}$: it is non-vanishing at finite normal distance and vanishes in the intrinsic boundary limit. The equal-time commutators of the boundary current with the spatial components of the gauge-invariant field strength vanish, so microcausality is satisfied; when the boundary parameters are such that the two boundary sectors decouple, its retarded response vanishes at all times. Locally, the boundary constraints are solved by $w_i=\partial_i\chi$ and $h_{ij}=\partial_i\partial_j\xi+\eta_{ij}\phi$. When the boundary parameters are such that the two sectors decouple, the induced action is the direct sum of a chiral boson in the $w_i$ sector and a higher-rank sector in which $\phi$ is auxiliary and $\psi=\partial_1\xi$ is the propagating field. The latter has a non-chiral Luttinger description on its positive-energy branch and admits a chiral reduction. The boundary conditions determine the velocity and positivity branch of the $w_i$ mode, while the compatibility analysis in the $h_{ij}$ sector selects the positive-energy branch. On the positive-energy branch the two chiral modes co-propagate with orientation opposite to the sign of $\kappa$.

Weakly conducting spheres suspended in a leaky dielectric fluid can undergo spontaneous Quincke rotation when the applied electric field exceeds a critical value. We investigate how electric and hydrodynamic interactions modify this instability and the subsequent rotation of two spheres at fixed separation and orientation. Starting from electric dipole and hydrodynamic rotlet interactions, we develop a systematic far-field asymptotic theory. Away from onset, slow drift of the rotation axes makes a regular expansion fail at long times. A multiple-scale expansion gives slow phase equations that select the axes according to pair orientation and field strength. Near onset, weak interactions produce corrections comparable to the isolated rotation magnitude. A detuned multiple-scale expansion gives coupled equations for the transverse dipole amplitudes. Their linearization identifies four collective rotation modes, whose critical fields and steady branches with one active mode are determined together with their stability. At leading order near onset, electric interaction shifts all four modal thresholds equally, whereas hydrodynamic interaction makes counter-rotation appear first for pair angles below $\cos^{-1}(1/\sqrt3)\simeq54.7^\circ$ and co-rotation above it. Away from onset, the angle separating stable counter-rotation from stable co-rotation increases with field strength. Boundary element method (BEM) simulations place onset within a field interval for each configuration and resolve the growth and relaxation of rotation. Steady-speed comparisons show how pair orientation changes the balance between electric and hydrodynamic effects. We compare the unexpanded dipole-rotlet model of Das and Saintillan [Phys. Rev. E 87, 043014 (2013)] with our asymptotic theory and BEM simulations.

Different ecological processes operate at different spatial and temporal scales. Macroscopic regularities can therefore be captured by descriptions that ignore microscopic details, even when those details are mechanistically relevant to ecological processes. Here, we develop a framework inspired by statistical mechanics to track interspecific spatial correlations under spatial coarse-graining. To do so we combine random-matrix filtering with a spatially explicit neutral model. Applying this approach to eight censuses of the Barro Colorado Island tropical forest, we observe a continuous crossover from an interacting to an effectively neutral organization. Below a few tens of metres (20--35~m), the empirical correlation spectrum differs from neutral expectations, revealing scale-dependent species-specific structure. Part of this structure can be attributed to environmental heterogeneity. However, residual spatial associations provide candidate signatures of biotic interactions or other unmeasured ecological, non-neutral processes. With increasing spatial coarse-graining, empirical and neutral correlation spectra progressively converge, and above the crossover scale the neutral model provides an accurate description of the measured collective organization. Neutrality thus emerges as an effective description of the collective organization of the forest above a characteristic scale, without implying that species are equivalent at the individual level. Our framework provides an operational way to locate that scale.

Chess openings naturally separate into slow and fast degrees of freedom: pawns evolve through irreversible moves, whereas pieces can be rapidly reorganized within the resulting structure. We exploit this separation to construct a quantitative morphology of opening space. From a catalogue of 3810 named variations, 1749 reach a common depth of $N=10$ plies, corresponding to 619 distinct positions and only 435 joint pawn structures. We characterize these positions through observables measuring pawn commitment and spatial organization, blockade and tension, and piece activity and centralization. Their partial independence reveals a multidimensional opening space and in order to explore its structural organization, we construct a network whose nodes are distinct White pawn structures, connected when a single pawn move or capture transforms one into another. Remarkably, 139 of the 149 observed structures belong to a single connected component containing $98\%$ of all positions. This network exhibits a statistically significant modular organization, with eight communities whose representative structures correspond to familiar pawn formations. Rather than forming isolated categories, these formations emerge as distinct regions of a connected structural landscape. Our approach thus complements the traditional opening taxonomy by revealing similarities between differently named openings and providing a quantitative basis for comparing the positions they produce.

When does a quantum particle arrive at a detector? The temporal distributions of itinerant quantum particles have been debated since the birth of quantum mechanics. Here we study the arrival-time problem in periodically monitored spin chains and quantum circuits. The arrival dynamics exhibits two regimes, the quantum Zeno and the low-monitoring regime, separated by an optimal monitoring period set by the single-particle bandwidth. In support of the theory, on superconducting quantum hardware, we measure arrival-time distributions for single and multiple interacting particles in one- and two-dimensional circuits. The measured distributions resolve both regimes and agree closely with quantum-trajectory theory. The crossover persists in interacting many-particle systems: the optimal monitoring point is preserved while many-body interference reshapes the distributions. Zeno suppression likewise persists in two-dimensional geometry. Together, these results show that the two regimes are a generic feature of monitored propagation rather than a single-particle effect. To our knowledge, our work constitutes the first experimental measurement of arrival-time distributions in a monitored quantum transport setting, addressing one of the longest-standing problems in quantum mechanics.

Compact analytical descriptors connect materials properties with interpretable combinations of physical and chemical variables, yet different expressions can capture similar trends in small datasets. We present a conditional Bayesian framework for quantifying competition among symbolic descriptors retained by the Sure Independence Screening and Sparsifying Operator (SISSO) method. Exact enumeration of fixed-size supports within the screened feature union yields posterior support probabilities, feature inclusion probabilities, and Bayesian-model-averaged predictions. Applied to magnetic moments of 88 full-Heusler alloys, the framework reveals substantial descriptor non-uniqueness even when the maximum-a-posteriori support coincides with deterministic SISSO. At both two and three descriptor dimensions, eight supports are required to accumulate 95\% posterior probability. Two prominent two-dimensional coordinates exhibit a Pearson correlation of 0.943 despite their distinct algebraic forms. Five-fold validation with screening repeated within each training fold shows higher prediction errors for Bayesian model averaging and undercoverage of nominal predictive intervals, separating descriptor competition from predictive performance. By making statistically competitive expressions explicit, the framework complements deterministic symbolic regression and provides a probabilistic basis for interpreting composition-property relationships in materials modeling.

arXiv:1303.7276v2 Announce Type: replace-cross Abstract: Achieving effective locomotion on diverse terrestrial substrates can require subtle changes of limb kinematics. Biologically inspired legged robots (physical models of organisms) have shown impressive mobility on hard ground but suffer performance loss on unconsolidated granular materials like sand. Because comprehensive limb-ground interaction models are lacking, optimal gaits on complex yielding terrain have been determined empirically. To develop predictive models for legged devices and to provide hypotheses for biological locomotors, we systematically study the performance of SandBot, a small legged robot, on granular media as a function of gait parameters. High performance occurs only in a small region of parameter space. A previously introduced kinematic model of the robot combined with a new anisotropic granular penetration force law predicts the speed. Performance on granular media is maximized when gait parameters minimize body acceleration and limb interference, and utilize solidification features of granular media.

arXiv:2609.31934v2 Announce Type: replace-cross Abstract: Overcoming experimental errors is a central challenge in quantum science. This challenge is particularly acute in large and complex quantum circuits, where quantum information spreads into exponentially many paths, foiling any direct attempt to understand errors' impact. In this work, we present a novel approach to understanding and mitigating experimental errors, based on a surprisingly compact representation of a quantum circuit's information dynamics, the reactivity function. The shape of a circuit's reactivity function governs its noise response, and its amenability to different error mitigation methods. From this viewpoint, we introduce two complementary such methods. The first, Pauli-path zero-noise extrapolation, fits a parameterized model to a circuit's reactivity function and uses it to accurately extrapolate to zero noise. The second, tunable error cancellation, filters a circuit's reactivity function to cancel noise on all information up to a threshold locality. Crucially, both methods feature a tuning parameter that allows one to systematically improve their accuracy until convergence. Across three circuit families from published experiments, our methods overcome conventional zero-noise extrapolation biases as large as 30%; at $\sim$$10^{-2}$ root-mean-square error, they reduce sampling cost relative to probabilistic error cancellation by up to a factor of $10^3$.

arXiv:2611.00422v2 Announce Type: replace-cross Abstract: We study how the layers in deep neural networks (NNs) converge, using Wilsonian Renormalization-Group (RG) ideas to organize the spectral picture. During training, these layers often develop heavy-tailed power-law (PL) spectra, and the strongest checkpoints often appear near the PL exponent $\alpha\approx 2$. This pattern raises a simple question: why should this value mark a well-trained layer? The answer is both statistical and physical. Our statistical hypothesis is that $\alpha=2$ marks the boundary between stable if not optimal learning and overfitting via non-self-averaging. The physical answer is that the same value makes the spectral energy gain scale evenly across logarithmic spectral scales, which is the proposed Wilsonian marginal condition. We then apply the ERG trace-log condition, the proposed SETOL theory, which we justify by taking volume-preserving, scale-invariant transformations to remove arbitrary layer scale along the proposed RG flow. The resulting spectral RG flow connects the HTSR and SETOL theories to optimizers such as Muon, and motivates a new optimizer extension, WW-PGD. Together, these results point toward a spectral Renormalization-Group view of learning, in which NNs may approach shared spectral structure in the settings studied here.

Scientific Reports, Published online: 08 November 2026; doi:10.1038/s41598-026-77224-y

Estimating dispersal, survival and population size of wild Aedes aegypti in Dar es Salaam, Tanzania using self-mark-release-recapture method

Communications Materials, Published online: 07 November 2026; doi:10.1038/s43246-026-01379-4

Narrowband multicolor lasing is crucial for advancing bioimaging, biosensing, and optoelectronic displays, yet current photonic crystal substrates face challenges in biocompatibility and energy efficiency. Here, the authors achieve narrowband multicolor lasing by coupling quantum dot emission with bamboo-derived photonic crystals, enhancing biocompatibility and biodegradability while simplifying fabrication, thus expanding applications in biomedicine and sustainable optoelectronics.

The sign problem in path integrals severely limits the application of quantum Monte Carlo methods to strongly correlated systems, whereas the Lefschetz-thimble method offers a rigorous framework to mitigate this issue. In this paper, we establish a numerical framework based on the Lefschetz thimbles for the Sachdev-Ye-Kitaev (SYK) model. By introducing continuous auxiliary fields via the Hubbard-Stratonovich transformation, the partition function is formulated as a high-dimensional complex integral. We employ the complex Langevin equation to explore the saddle-point distribution of the effective action in the complex plane. Monte Carlo integration is then performed to compute the partition function and Green functions. Our numerical results exhibit excellent agreement with high-temperature expansions, infrared-limit solutions, and determinantal quantum Monte Carlo (DQMC) simulations, confirming the validity of our framework. Furthermore, we demonstrate that our complex Langevin search successfully captures the relevant dominant saddle points governing the SYK model in the large-N limit. Our work deepens the understanding of the sign problem in the SYK model and provides a viable non-perturbative avenue for addressing sign problems in more complex strongly correlated systems.

We propose a remote detectability criterion for two-dimensional conformal field theories, which asserts that any local operator outside of the product of the left- and right-moving Virasoro algebras can be detected by some topological line defect. We discuss its relationship to existing results in the conformal net literature. We then use this criterion to argue that the known $SU(2)$ moduli space of unitary conformal boundary conditions and the $SO(4)$ moduli space of unitary topological line defects of the $SU(2)_1$ Wess-Zumino-Witten model completely capture all unitary conformal boundaries and unitary topological lines of the theory. Invoking the fact that the non-compact boson conformal field theory can be obtained from $SU(2)_1$ by "flat-gauging" a $U(1)$ symmetry, we are also able to completely classify the unitary conformal boundaries and unitary topological line defects of the two-dimensional free scalar field. In particular, we find a 4-dimensional moduli space of topological line defects, most of which were not known previously. We support our proposed classifications by writing down concrete Lagrangian descriptions of all of the boundaries and lines of the non-compact boson. For every boundary condition, we calculate the corresponding boundary state, and for each pair of boundary conditions, we calculate the corresponding interval Hilbert space. We verify that the annulus partition functions of the theory respect open/closed duality. We also calculate the fusion rules of the topological line defects, their action on local operators, their action on the boundary conditions by parallel fusion, and their corresponding twisted-sector Hilbert spaces.

We analytically compute the longitudinal charged-current correlator in a near-extremal holographic plasma with quark and isospin chemical potentials, $\mu_q$ and $\mu_3$ respectively. To this end, we study fluctuations of gauge fields around a low-temperature AdS$_5$ Reissner-Nordstr\"om black hole charged both under the quark number and the isospin. The result is obtained at next-to-leading order in a hydrodynamic expansion where apart from the temperature and isospin chemical potential, the frequency and momenta are small compared to the quark chemical potential, $\omega,k,T,\mu_3\ll\mu_q$. This approach captures the interplay between the hydrodynamic-like pole and the tower of infrared modes produced by the AdS$_2$ throat controlling the geometry of the black hole near extremality. At zero isospin chemical potential, the resulting quasinormal-mode formula reproduces the collision of the diffusive pole with the infrared spectrum, while the finite isospin chemical potential lifts this collision. The analytic spectrum agrees precisely with the full numerical results. The next-to-leading-order correlator also substantially improves the spectral function beyond the standard hydrodynamic regime $\omega,k,\mu_3\ll T$, extending the agreement with numerics to larger frequencies and momenta.