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arXiv2024

State Dependent Spread Complexity Dynamics in Many-Body Localization Transition

We characterize the Many-Body Localization (MBL) phase transition using the dynamics of spread complexity and inverse participation ratio in the Krylov space starting from different initial states. Our analysis of the disordered Heisenberg spin-1/2 chain unravels that the ergodic-to-MBL transition can be determined from the transition of the pre-saturation peak in the thermofield double state (TFD) spread complexity. On the other hand, if an initially ordered state or a superposition of a small number of such states is chosen, then the saturation value of spread complexity and Krylov inverse participation ratio (KIPR) can distinguish the ergodic phase from the integrable phases, with no sharp difference between the integrable phases. Interestingly, the distinction between the disorder-free integrable and the MBL integrable phase is established by the spread complexity study of random states chosen from unitary and orthogonal Haar ensembles. We also study the complexity dynamics by coupling the system to a bath, which shows distinctive profiles in different phases. A stretched exponential decay of KIPR is observed when the MBL system is connected to the bath, with the decay starting at an earlier time for a greater value of environmental dephasing. Our work sheds light on the efficacy of Krylov space dynamics in understanding phase transitions in quantum many-body systems.

cond-mat.dis-nn↗

arXiv2024

Exploring Metallic-Insulating Transition and Thermodynamic Applications of Fibonacci Quasicrystals

Extended and critical states are two common phenomena in Fibonacci quasicrystals. In this paper, we first reveal the difference between the extended phase and the critical phase in the extended-critical Fibonacci quasicrystal from the perspectives of quantum transport and Wigner distribution. The transport conductance indicates that the extended-critical transition resembles a metallic-insulating transition. Moreover, the Wigner distributions show that the Wigner distribution of the extended wave function is localized in the momentum direction of the phase space, while that of the critical wave function is sub-extended in the momentum direction of the phase space. Based on the results of entanglement entropy, the extended-critical transition is a thermodynamic phase transition because it is accompanied by decreasing entropy. We engineer a quantum heat cycle engine with the extended-critical quasicrystal as the working medium, and find that there are rich working modes in the engine, such as quantum accelerator, quantum heater and quantum heat engine. Importantly, the extended quasicrystals are more conducive to the realization of quantum heat engines, while the critical quasicrystals are more conducive to the realization of quantum heaters. Our work is an important step toward exploring the rich thermodynamic applications of Fibonacci quasicrystals.

cond-mat.dis-nn↗

arXiv2025

On the nature of the glass transition in metallic glasses after deep relaxation

We performed parallel study of calorimetric and high-frequency shear modulus behavior of Zr-based metallic glasses after deep relaxation just below the glass transition. It is shown that deep relaxation results in the appearance of a strong peak of the excess heat capacity while the shear modulus is moderately affected. A theory assuming high-frequency shear modulus to be a major physical parameter controlling glass relaxation is suggested. The energy barrier for these rearrangements is proportional to the shear modulus while its magnitude, in turn, varies due to the changes in the defect concentration (diaelastic effect). Both dependences lead to the occurrence of heat effects. The excess heat capacity calculated using experimental shear modulus data demonstrates very good agreement with the experimental calorimetric data for all states of glasses. It is argued that the glass transition behavior after deep relaxation of glass is close to a phase transition of the first kind.

cond-mat.dis-nn↗

arXiv2025

Signal amplification in a solid-state quantum sensor via asymmetric time-reversal of many-body dynamics

Electronic spins of nitrogen vacancy (NV) centers in diamond constitute a promising system for micro- and nano-scale magnetic sensing, due to their operation under ambient conditions, ease of placement in close proximity to sensing targets, and biological compatibility. At high densities, the electronic spins interact through dipolar coupling, which typically limits but can also potentially enhance sensing performance. Here we report the experimental demonstration of many-body signal amplification in a solid-state, room temperature quantum sensor. Our approach utilizes time-reversed two-axis-twisting interactions, engineered through dynamical control of the quantization axis and Floquet engineering in a two-dimensional ensemble of NV centers. Strikingly, we observe that the optimal amplification occurs when the backward evolution time equals twice the forward evolution time, in sharp contrast to the conventional Loschmidt echo. These observations can be understood as resulting from an underlying time-reversed mirror symmetry of the microscopic dynamics, providing key insights into signal amplification and opening the door towards entanglement-enhanced practical quantum sensing.

quant-ph↗

arXiv2025

Dislocations in the elastic fields of randomly distributed defects

In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation and compression centers. More generally speaking, the arrangement of defects in metals and alloys is always characterized by statistical disorder, and the same is true for the fluctuating fields that arise from the superposition of the stress and strain fields of many defects. In order to develop models for the dynamics of dislocations interacting with such fields, a statistical description of the dislocation energy landscape and the associated configurational forces is needed, as well as methods for coarse graining these forces over dislocation segments of varying length and shape. In this context the problem arises how to regularize the highly singular stress fields associated with dislocations and other defects. Here we formulate an approach which is based upon evaluating the interaction energies and interaction forces between singular dislocations and other defects including solutes, modelled as point-like dilatation centers, and other dislocations. We characterize the interactions in terms of the probability densities of interaction energies and interaction forces, and the corresponding spatial correlation functions. We also consider the effects of dislocation core regularization, either in terms of continuously distributed Burgers vectors or by using the formalism of gradient elasticity of Helmholtz type to formulate a regularized energy functional.

cond-mat.mtrl-sci↗

arXiv2025

Cooperative atomic motion during shear deformation in metallic glass

Elucidating mechanical deformation in glassy materials at the atomic level is challenging due to their disordered atomic structure. Using our novel "frozen atom analysis," we reveal that anelastic deformation in CuZr metallic glasses is fundamentally driven by cooperative atomic motions of approximately 40 elastically linked atoms, forming trigger groups. They initiate localized rearrangements, which can cascade into plastic flow. Notably, these groups show no distinct structural or physical features, challenging the idea that deformation occurs in defective regions. Instead, deformation events are highly stochastic and transient, driven by collective atomic motion. This finding not only reshapes our understanding of glassy material deformation mechanisms but also highlights cooperative motion as a key factor in avalanche-like phenomena governing the behavior of disordered systems across multiple scales.

cond-mat.mtrl-sci↗

arXiv2026

Role of scrambling and noise in temporal information processing with quantum systems

Scrambling quantum systems have attracted attention as effective substrates for temporal information processing. Here we consider a quantum reservoir processing framework that captures a broad range of physical computing models with quantum systems. We examine the scalability and memory retention of the model with scrambling reservoirs modelled by high-order unitary designs in both noiseless and noisy settings. In the former regime, we show that measurement readouts become exponentially concentrated with increasing reservoir size, yet strikingly do not worsen with the reservoir iterations. Thus, while repeatedly reusing a small scrambling reservoir with quantum data might be viable, scaling up the problem size deteriorates generalization unless one can afford an exponential shot overhead. In contrast, the memory of early inputs and initial states decays exponentially in both reservoir size and reservoir iterations. In the noisy regime, we also prove that memory decays exponentially in time for local noisy channels. These results required us to introduce new proof techniques for bounding concentration in temporal quantum models. Beyond this extreme scrambling regime, we numerically demonstrate that exponential concentration can still exist even with a physical reservoir such as an Ising model whenever the reservoir operates in a quantum-chaotic phase. In contrast, physical reservoirs in a many-body localized phase and at the edge of chaos appear to not suffer from such phenomena

quant-ph↗

arXiv2026

On the origin of neural scaling laws: from random graphs to natural language

Scaling laws have played a major role in the modern AI revolution, providing practitioners predictive power over how the model performance will improve with increasing data, compute, and number of model parameters. This has spurred an intense interest in the origin of neural scaling laws, with a common suggestion being that they arise from power law structure already present in the data. In this paper we study scaling laws for transformers trained to predict random walks (bigrams) on graphs with tunable complexity. We demonstrate that this simplified setting already gives rise to neural scaling laws even in the absence of power law structure in the data correlations. We further consider dialing down the complexity of natural language systematically, by training on sequences sampled from increasingly simplified generative language models, from 4,2,1-layer transformer language models down to language bigrams, revealing a monotonic evolution of the scaling exponents. Our results also include scaling laws obtained from training on random walks on random graphs drawn from Erdös-Renyi and scale-free Barabási-Albert ensembles. Finally, we revisit conventional scaling laws for language modeling, demonstrating that several essential results can be reproduced using 2 layer transformers with context length of 50, provide a critical analysis of various fits used in prior literature, demonstrate an alternative method for obtaining compute optimal curves as compared with current practice in published literature, and provide preliminary evidence that maximal update parameterization may be more parameter efficient than standard parameterization.

cs.LG↗

arXiv2026

A Physics-Regularized Neural Network and Kirchhoff Markov Random Field Framework for Inferring Internal Electrochemical States from Operando Spectromicroscopy

Quantitative understanding of coupled reaction-transport dynamics in lithium-ion battery (LIB) composite electrodes is limited by the inaccessibility of key internal electrochemical states. Here we present a physics-integrated, data-driven framework to reconstruct latent states from operando microscopic X-ray absorption fine structure ($μ$ -XAFS) hyperspectral data of LIB cathodes. Normalized-local-lithium-stoichiometry (NLLS) maps derived from Co K-edge spectra are refined using a physics-regularized neural network that enforces spatial continuity and current conservation to resolve ambiguities in the weak-sensitivity region. The reconstructed NLLS dynamics are embedded in a Kirchhoff-based Markov random field incorporating Kirchhoff's laws, Ohm's law, and Butler-Volmer kinetics to infer interfacial current density, ionic current, electrolyte potential, and effective ionic conductivity. Application to electrodes with differential initial electrolyte concentrations reveals distinct reaction-propagation modes that are consistent with a mechanism involving the non-monotonic concentration dependence of electrolyte conductivity. The inferred electrolyte concentration profiles qualitatively resemble the spatially extended concentration changes observed by independent operando X-ray transmission imaging using a 1 M LiAsF$_6$ electrolyte.

physics.chem-ph↗

arXiv2026

Reducibility of native weighted graphs on Rydberg Arrays

We investigate the classical reducibility of random unit-disk graph (UDG) instances of the maximum independent set (MIS) and maximum weighted independent set (MWIS) problems, which can be natively realised in Rydberg atom quantum processors. Using state-of-the-art kernelisation techniques, we systematically probe how far classical preprocessing can simplify such native optimisation problems of varying size and connectivity. While many small or sparse instances can be fully reduced, dense graphs often retain finite irreducible kernels even after extensive reductions. Introducing vertex weights tends to increase reducibility, whereas extending the interaction range in the underlying UDG connectivity suppresses the reduction efficiency. By exploring where classical reductions cease to be effective, we aim to delineate the regime of problem instances that remain computationally demanding - those most relevant for testing and benchmarking near-term quantum optimisation hardware. We find that for the remaining finite kernels, quantum execution would require non-native embeddings with substantial resource overheads, suggesting that directly running native instances may be more practical than embedding a reduced kernel.

quant-ph↗

arXiv2026

On the robustness of noisy solutions in non-convex neural networks

Optimization in non-convex neural network models is strongly influenced by the geometry of the solution space: sparse, isolated, point-like clusters are typically algorithmically inaccessible, whereas wide and flat regions can be found efficiently despite being relatively rare. At zero temperature this picture has been formalized in binary perceptrons through the overlap gap property (OGP), which limits algorithmic access to configurations with zero training error above a critical constraint density $α_{\rm OGP}$. Here we extend this description to finite temperature, where a positive training error is allowed and statistically penalized. We first show that the frozen one-step replica-symmetry-breaking solution, dominating the zero temperature equilibrium measure, survives at any finite temperature. We furthermore derive a general criterion, based on the smoothness of the single-pattern Gibbs weight near the decision boundary, that determines when a finite-temperature relaxation of the loss removes freezing. We then extend the OGP construction to finite temperature and show that dense, algorithmically accessible regions of finite-energy configurations persist beyond $α_{\rm OGP}$, up to a threshold $α_{\rm OGP}(ε)$ that grows with the allowed training error $ε$. Finally, in the teacher-student setting, we show that these wide, finite-energy regions still retain good generalization. Using a finite energy message-passing algorithm, we demonstrate numerically that thermal noise enables effective generalization in the regime of constraint densities where both recovering the teacher and finding a zero temperature solution are computationally hard.

cond-mat.dis-nn↗

arXiv2026

Quantum geometric localization length and localization criticality in an ideally flat Chern band

We propose that the localization length in an isolated, ideally flat Chern band is set by quantum geometry. We explore the corresponding localization transition and its critical scaling by applying transfer matrix calculations in the maximally localized hybrid Wannier basis, whose spatial spread is exactly characterized by a quantum geometric length. Remarkably, upon tuning the quantum metric of the Chern band, we observe a crossover from a universal regime controlled by the Dirac fixed point to a non-universal regime with continuously varying critical exponents. Within the universal regime, the localization length exhibits a pronounced linear dependence on the quantum geometric length, supporting its quantum geometric nature. These findings provide a novel quantum geometric perspective on the localization in quantum Hall systems such as twisted moiré superlattices, and shed new light on the long-standing controversy over the criticality of the integer quantum Hall transition.

cond-mat.str-el↗

arXiv2026

Unifying Physical Backpropagation

Physical computing systems exploit device dynamics for computation, but their gradient-based optimization is challenging: backpropagation through a digital twin suffers from a model-reality gap. On-device gradient computation could resolve this issue, and a handful of theoretical and experimental studies have proposed ways to achieve it. Yet a unifying theory identifying when a physical system can compute the gradient of its own performance has been missing. Here we develop such a unification based on the adjoint method: we identify sufficient conditions under which the adjoint field required for formally exact gradients can be generated on the same hardware that performs the computation. Linear and nonlinear systems obey fundamentally different conditions: for linear systems, damping or gain is admissible provided reciprocity is preserved. For nonlinear trajectory systems, the sufficient conditions are reciprocity of the linearized system and the existence of a time-reversal mirror. Algorithmically, the nonlinear case requires infinitesimal nudging, whereas linear systems admit a finite-amplitude experiment. We recover (quantum) Equilibrium Propagation, Hamiltonian echo backpropagation, fully forward mode training and in situ gradient methods in integrated-photonic and free-space-optical systems. Finally, we show that reciprocity is a special case of more general intertwining conditions. For linear systems, these permit exact on-device gradients in a class of non-Hermitian, non-reciprocal systems. For nonlinear trajectories, they combine with generalized time-reversal mirrors to cover, e.g., PT-symmetric equations. The framework also includes time-dependent parameters and Onsager-reciprocal dynamics, providing a unified basis for formally exact physical learning.

cond-mat.dis-nn↗

arXiv2026

Discrete Diffusion Models via Evolving Variational Autoregressive Networks

Conventional score-based diffusion models learn scores without representing normalized densities, whereas tractable normalized models support both sampling and direct likelihood evaluation. A recent tensor-network approach provides such a representation but is largely restricted to low-dimensional lattices. Here we introduce a discrete diffusion model that parameterizes normalized probability distributions using variational autoregressive networks. Explicit Markov jump operators govern the forward noising and reverse denoising dynamics, extending discrete diffusion models with normalized distributions to spin systems on higher-dimensional lattices. We apply this framework to the two- and three-dimensional Ising models across ordered, critical, and disordered regimes, accurately computing thermodynamic quantities including free energy, energy, and magnetization. We further integrate the framework with Monte Carlo sampling, using adaptive diffusion steps to maintain high acceptance rates even at low temperatures while enhancing sample diversity. These results establish a neural-network framework for the discrete diffusion model with normalized probability distributions.

cs.LG↗

arXiv2026

Optimal low-rank compression of quantum dynamics

Local quantum interactions generate dynamics in an exponentially large Hilbert space, yet locality and entanglement restrict the information that can spread and accumulate. Bounds on propagation and entanglement growth, together with tensor networks, exploit these restrictions to discard information unnecessary for describing the evolution. This leads to a sharper question: how much information must any low-rank representation retain? Here we determine these limits, up to logarithmic factors, for short-range interactions. For time-independent evolution, the optimal rank obeys $\log D=\widetilde O(t+\sqrt{\log(1/ε)})$, with matching lower bounds fixing the accuracy exponent $1/2$; for arbitrary driving, matching fixed-time bounds instead give $2/3$. Correspondingly, the corresponding dynamical entanglement spectra exhibit distinct small-$α$ Rényi laws, $α^{-1}$ and $α^{-2}$. In one dimension, the static limit is constructively attained by an explicit MPO algorithm, with an analogous extension to Liouvillian dynamics. Together, these results determine the irreducible information required to represent local quantum evolution and uncover distinct entanglement structures in static and driven dynamics.

quant-ph↗

arXiv2026

Correlated quasiperiodicity enables efficient thermoelectric energy conversion

We investigate a route to enhanced thermoelectric energy conversion in nanoscale systems by exploiting a correlated quasiperiodic energy landscape in a one-dimensional chain coupled to source and drain reservoirs. The considered modulation generates a highly non-uniform electronic transmission spectrum, providing favorable conditions for achieving a large thermoelectric figure of merit. By systematically tuning the incommensurability parameter, a variety of quasiperiodic configurations are explored, several of which yield high values of the figure of merit exceeding $2$. Electronic transport properties are evaluated within a tight-binding framework using the non-equilibrium Green's function formalism, while the thermoelectric coefficients, including electrical conductance, Seebeck coefficient, and electronic thermal conductance, are determined through the Landauer approach. The underlying quasiperiodic potential belongs to the Aubry-André-Harper (AAH) family and exhibits a weakly varying spatial profile, leading to transmission characteristics that are favorable for thermoelectric optimization. The influence of phonon thermal conductance on the overall energy-conversion efficiency is also analyzed in detail. For the sake of completeness, we also critically inspect the effect of conductor to electrode coupling and the coupling asymmetry on $ZT$. We also check the thermoelectric response of conventional AAH system and an elaborate comparison is made with our chosen quantum system. Our findings highlight the potential of correlated quasiperiodic nanostructures as promising candidates for efficient thermoelectric applications.

cond-mat.mes-hall↗

arXiv2026

Rank-One Signal Recovery in Sparse Wishart Noise

We study the high-dimensional recovery of a signal vector $\mathbf{x}$ in the presence of sparse Wishart-like noise. We define an $N \times N$ matrix $A = J+(θ/N)\mathbf{xx}^{\top}$, where $\mathbf{xx}^{\top}$ is the rank-one deformation of the random noise matrix $J$. We consider a Wishart-like matrix $J={X}^{\top} X$, where $X$ is a sparse $M \times N$ random matrix with entries $X_{ij} = c_{ij}W_{ij}$, with $c_{ij}$ regulating the density of non-zero elements, and $W_{ij}$ the bond weights. Using the replica method, we compute analytically the top eigenpair statistics of $A$, and their dependence on the signal strength $θ$, the rectangularity ratio $α=\sqrt{M/N}$, and the average connectivity of the noise. The spectral observables are expressed in terms of a system of Recursive Distributional Equations, which are efficiently solved via a Population Dynamics algorithm. They allow us to compute the average largest eigenvalue $\langleλ_1\rangle_{A}$, the average top eigenvector component density, and the average overlap between the top eigenvector of $A$ and $\mathbf{x}$. We identify a critical threshold $θ_{\mathrm{crit}}$--depending on the average connectivity of the noise--that marks a BBP-like phase transition: below this value, $\langleλ_1\rangle_{A}$ is unaffected by the signal, and the overlap vanishes. Thus, the signal is not recoverable from the top eigenvector of $A$. For $θ>θ_{\mathrm{crit}}$, the signal-related outlier eigenvalue becomes $\langleλ_1\rangle_{A}$ and the overlap is nonzero, allowing for recovery of the signal. The results are in excellent agreement with numerical diagonalisation. We show that in the dense limit, the recovery threshold and eigen-statistics converge to the results predicted by the classical BBP transition for additive rank-one deformations of dense Wishart matrices.

cond-mat.dis-nn↗

arXiv2026

Local time-reversal-invariant topological markers in two dimensions

Local topological markers provide a real-space characterization of topological phases and are suited to noncrystalline models. We derive a local topological marker, the Chern-Simons descendant marker, for characterizing the topology of two-dimensional time-reversal-invariant near-Gaussian states from the one-particle density matrix $ρ$. We construct an auxiliary three-dimensional state characterized by the local Chern-Simons marker, and use dimensional reduction to obtain the Chern-Simons descendant marker for the original two-dimensional state. This derivation introduces a local Hermitian involution $S$ that is odd under time reversal. When $[S,ρ]=0$, the local Chern-Simons descendant marker reduces to half the difference of the local Chern markers in the $S=\pm1$ sectors. Constructing an $S$ that commutes exactly with $ρ$ generally requires fine-tuning, but this is not needed---the local Chern-Simon marker remains well defined whenever $Γ=\{ρ,S\}-S$ has a spectral gap around zero, even when $[S,ρ]\neq0$. This leaves the practical problem of identifying a suitable $S$ for a given state, which, importantly, is straightforward even when spin is not a candidate. We show this by considering both strong Rashba and Dresselhaus spin-orbit coupling, for which knowledge of the physical origin of the state reduces the general problem of choosing $S$ to a one-parameter family $S(θ)$. We evaluate the optimal angle $θ$ maximizing the spectral gap of $Γ$ analytically assuming translation invariance, and find that the gap of $Γ$ remains open for a broad range of angles around the optimum. The same value of $θ$ remains valid in disordered systems, providing an easy way to obtain choice of $S$ for evaluating the local Chern-Simons descendant marker of the state.

cond-mat.mes-hall↗