CyberSec Research

How are the spatial and temporal patterns of information scrambling in locally interacting quantum many-body systems imprinted on the eigenstates of the system's time-evolution operator? We address this question by identifying statistical correlations among sets of minimally four eigenstates that provide a unified framework for various measures of information scrambling. These include operator mutual information and operator entanglement entropy of the time-evolution operator, as well as more conventional diagnostics such as two-point dynamical correlations and out-of-time-ordered correlators. We demonstrate this framework by deriving exact results for eigenstate correlations in a minimal model of quantum chaos -- Floquet dual-unitary circuits. These results reveal not only the butterfly effect and the information lightcone, but also finer structures of scrambling within the lightcone. Our work thus shows how the eigenstates of a chaotic system can encode the full spatiotemporal anatomy of quantum chaos, going beyond the descriptions offered by random matrix theory and the eigenstate thermalisation hypothesis.

We study the charge and spin-dependent thermoelectric response of a ferromagnetic helical system irradiated by arbitrarily polarized light, using a tight-binding framework and the Floquet-Bloch formalism. Transport properties for individual spin channels are determined by employing the non-equilibrium Green's function technique, while phonon thermal conductance is evaluated using a mass-spring model with different lead materials. The findings reveal that that light irradiation induces spin-split transmission features, suppresses thermal conductance, and yields favorable spin thermopower and figure of merit (FOM). The spin FOM consistently outperforms its charge counterpart under various light conditions. Moreover, long-range hopping is shown to enhance the spin thermoelectric performance, suggesting a promising strategy for efficient energy conversion in related ferromagnetic systems.

We first present a comparative analysis of temperature evolution of the excess thermodynamic potentials (state functions), the enthalpy $\Delta H$, entropy $\Delta S$ and Gibbs free energy $\Delta \Phi$, determined for \textit{i}) undercooled melts using literature data and \textit{ii}) solid glassy state calculated on the basis of calorimetry measurements using an approach proposed recently. Three metallic alloys were taken as an example for data analysis. It is found that temperature dependences $\Delta H(T)$, $\Delta S(T)$ and $\Delta G(T)$ calculated with both approaches coincide in the supercooled liquid range (i.e. at temperatures $T_g<T<T_x$, where $T_g$ and $T_x$ are the glass transition and crystallization onset temperatures, respectively). However, the necessary conditions for this coincidence is the introduction of important changes to the above approach \textit{i}), which are related to the calculation of the melting entropy. We also introduce and calculate a dimensionless order parameter $\xi$, which changes in the range $0<\xi<1$ and characterizes the evolution of the structural order from liquid-like to crystal-like one. It is shown that the order parameter $\xi_{scl}$ calculated for the end of the supercooled liquid range (i.e. for a temperature just below $T_x$) correlates with the melt critical cooling rate $R_c$: the smaller the order parameter $\xi_{scl}$ (i.e. the closer the structure to that of the equilibrium liquid), the smaller $R_c$ is.

We study analytically and numerically a Hopfield fully-connected network with $d$-vector spins. These networks are models of associative memory that generalize the standard Hopfield with Ising spins. We study the equilibrium and out-of-equilibrium properties of the system, considering the system in its retrieval phase $\alpha<\alpha_c$ and beyond. We derive the Replica Symmetric solution for the equilibrium thermodynamics of the system, together with its phase diagram: we find that the retrieval phase of the network shrinks with growing spin dimension, having ultimately a vanishing critical capacity $\alpha_c\propto 1/d$ in the large $d$ limit. As a trade-off, we observe that in the same limit vector Hopfield networks are able to denoise corrupted input patterns in the first step of retrieval dynamics, up to very large capacities $\widetilde{\alpha}\propto d$. We also study the static properties of the system at zero temperature, considering the statistical properties of soft modes of the energy Hessian spectrum. We find that local minima of the energy landscape related to memory states have ungapped spectra with rare soft eigenmodes: these excitations are localized, their measure condensating on the noisiest neurons of the memory state.

Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of techniques to address this challenge. In this work, we illustrate three of the main methods: the Maximum Likelihood, Maximum Pseudo-Likelihood, and Mean-Field approaches. We begin with a thorough theoretical introduction to these methods, followed by their application to inference in several well-known statistical physics systems undergoing phase transitions. Namely, we consider the ordered and disordered Ising models, the vector Potts model, and the Blume-Capel model on both regular lattices and random graphs. This discussion is accompanied by a GitHub repository that allows users to both reproduce the results and experiment with new systems.

In amorphous solids, frustrated elastic interactions conspire with thermal noise to trigger anomalously slow sequences of plastic rearrangements, termed "thermal avalanches", which play an important role during creep and glassy relaxations. Here we uncover the complex spatiotemporal structure of thermal avalanches in simulations of a model amorphous solid. We systematically disentangle mechanical and thermal triggering during logarithmic creep, revealing a hierarchy of fast localized cascades linked by slow, long-range, noise-mediated facilitation. These thermal avalanches exhibit heavy-tailed temporal correlations, reminiscent of seismic activity. Our work sheds light on the rich relaxation dynamics of amorphous solids, while providing a framework for identifying noise-mediated correlations. We validate this approach by revealing a similar hierarchy in experiments with crumpled thin sheets.

Crystalline topological insulator nanowires with a magnetic flux threaded through their cross section display Aharanov-Bohm conductance oscillations. A characteristic of these oscillations is the perfectly transmitted mode present at certain values of the magnetic flux, due to the appearance of an effective time-reversal symmetry combined with the topological origin of the nanowire surface states. In contrast, amorphous nanowires display a varying cross section along the wire axis that breaks the effective time-reversal symmetry. In this work, we use transport calculations to study the stability of the Aharanov-Bohm oscillations and the perfectly transmitted mode in amorphous topological nanowires. We observe that at low energies and up to moderate amorphicity the transport is dominated, as in the crystalline case, by the presence of a perfectly transmitted mode. In an amorphous nanowire the perfectly transmitted mode is protected by chiral symmetry or, in its absence, by a statistical time-reversal symmetry. At high amorphicities the Aharanov-Bohm oscillations disappear and the conductance is dominated by nonquantized resonant peaks. We identify these resonances as bound states and relate their appearance to a topological phase transition that brings the nanowires into a trivial insulating phase.

Our recent study on the Bethe lattice reported that a discontinuous percolation transition emerges as the number of occupied links increases and each node rewires its links to locally suppress the growth of neighboring clusters. However, since the Bethe lattice is a tree, a macroscopic cluster forms as an infinite spanning tree but does not contain a finite fraction of the nodes. In this paper, we study a bipartite network that can be regarded as a locally tree-like structure with long-range neighbors. In this network, each node in one of the two partitions is allowed to rewire its links to nodes in the other partition to suppress the growth of neighboring clusters. We observe a discontinuous percolation transition characterized by the emergence of a single macroscopic cluster containing a finite fraction of nodes, followed by critical behavior of the cluster size distribution. We also provide an analytical explanation of the underlying mechanism.

Non-equilibrium dynamics have become a central research focus, exemplified by the counterintuitive Mpemba effect where initially hotter systems can cool faster than colder ones. Studied extensively in both classical and quantum regimes, this phenomenon reveals diverse and complex behaviors across different systems. This review provides a concise overview of the quantum Mpemba effect (QME), specifically emphasizing its connection to symmetry breaking and restoration in closed quantum many-body systems. We begin by outlining the classical Mpemba effect and its quantum counterparts, summarizing key findings. Subsequently, we introduce entanglement asymmetry and charge variance as key metrics for probing the QME from symmetry perspectives. Leveraging these tools, we analyze the early- and late-time dynamics of these quantities under Hamiltonian evolution and random unitary circuits. We conclude by discussing significant challenges and promising avenues for future research.

We investigate the competing mechanisms of localisation in one-dimensional disordered block subwavelength resonator systems subject to nonreciprocal damping, induced by an imaginary gauge potential. Using a symmetrisation approach to enable the adaptation of tools from Hermitian systems, we derive the limiting spectral distribution of these systems as the number of blocks goes to infinity and characterise their spectral properties in terms of the spectral properties of their constituent blocks. By employing a transfer matrix approach, we then clarify, in terms of Lyapunov exponents, the competition between the edge localisation due to imaginary gauge potentials and the bulk localisation due to disorder. In particular, we demonstrate how the disorder acts as insulation, preventing edge localisation for small imaginary gauge potentials.

Accurate grain orientation mapping is essential for understanding and optimizing the performance of polycrystalline materials, particularly in energy-related applications. Lithium nickel oxide (LiNiO$_{2}$) is a promising cathode material for next-generation lithium-ion batteries, and its electrochemical behaviour is closely linked to microstructural features such as grain size and crystallographic orientations. Traditional orientation mapping methods--such as manual indexing, template matching (TM), or Hough transform-based techniques--are often slow and noise-sensitive when handling complex or overlapping patterns, creating a bottleneck in large-scale microstructural analysis. This work presents a machine learning-based approach for predicting Euler angles directly from scanning transmission electron microscopy (STEM) diffraction patterns (DPs). This enables the automated generation of high-resolution crystal orientation maps, facilitating the analysis of internal microstructures at the nanoscale. Three deep learning architectures--convolutional neural networks (CNNs), Dense Convolutional Networks (DenseNets), and Shifted Windows (Swin) Transformers--are evaluated, using an experimentally acquired dataset labelled via a commercial TM algorithm. While the CNN model serves as a baseline, both DenseNets and Swin Transformers demonstrate superior performance, with the Swin Transformer achieving the highest evaluation scores and the most consistent microstructural predictions. The resulting crystal maps exhibit clear grain boundary delineation and coherent intra-grain orientation distributions, underscoring the potential of attention-based architectures for analyzing diffraction-based image data. These findings highlight the promise of combining advanced machine learning models with STEM data for robust, high-throughput microstructural characterization.

Topological invariants, such as the winding number, the Chern number, and the Zak phase, characterize the topological phases of bulk materials. Through the bulk-boundary correspondence, these topological phases have a one-to-one correspondence to topological edge states, which are robust to certain classes of disorder. For simple models like the Su-Schrieffer-Heeger (SSH) model, the computation of the winding number and Zak phase are straightforward, however, in multiband systems, this is no longer the case. In this work, we introduce the unwrapped Wilson line across the Brillouin zone to compute the bulk topological invariant. This method can efficiently be implemented numerically to evaluate multiband SSH-type models, including models that have a large number of distinct topological phases. This approach accurately captures all topological edge states, including those overlooked by traditional invariants, such as the winding number and Zak phase. To make a connection to experiments, we determine the sign of the topological invariant by considering a Hall-like configuration. We further introduce different classes of disorder that leave certain edge states protected, while suppressing other edge states, depending on their symmetry properties. Our approach is illustrated using different one-dimensional models, providing a robust framework for understanding topological properties in one-dimensional systems.

We study the statistical properties of the physical action $S$ for random graphs, by treating the number of neighbors at each vertex of the graph (degree), as a scalar field. For each configuration (run) of the graph we calculate the Lagrangian of the degree field by using a lattice quantum field theory(LQFT) approach. Then the corresponding action is calculated by integrating the Lagrangian over all the vertices of the graph. We implement an evolution mechanism for the graph by removing one edge per a fundamental quantum of time, resulting in different evolution paths based on the run that is chosen at each evolution step. We calculate the action along each of these evolution paths, which allows us to calculate the probability distribution of $S$. We find that the distribution approaches the normal(Gaussian) form as the graph becomes denser, by adding more edges between its vertices. The maximum of the probability distribution of the action corresponds to graph configurations whose spacing between the values of $S$ becomes zero $\Delta S=0$, corresponding to the least-action (Hamilton) principle, which gives the path that the physical system follows classically. In addition, we calculate the fluctuations(variance) of the degree field showing that the graph configurations corresponding to the maximum probability of $S$, which follow the Hamilton's principle, have a balanced structure between regular and irregular graphs.

Imaging techniques such as functional near-infrared spectroscopy (fNIRS) and diffuse optical tomography (DOT) achieve deep, non-invasive sensing in turbid media, but they are constrained by the photon budget. Wavefront shaping (WFS) can enhance signal strength via interference at specific locations within scattering media, enhancing light-matter interactions and potentially extending the penetration depth of these techniques. Interpreting the resulting measurements rests on the knowledge of optical sensitivity - a relationship between detected signal changes and perturbations at a specific location inside the medium. However, conventional diffusion-based sensitivity models rely on assumptions that become invalid under coherent illumination. In this work, we develop a microscopic theory for optical sensitivity that captures the inherent interference effects that diffusion theory necessarily neglects. We analytically show that under random illumination, the microscopic and diffusive treatments coincide. Using our microscopic approach, we explore WFS strategies for enhancing optical sensitivity beyond the diffusive result. We demonstrate that the input state obtained through phase conjugation at a given point inside the system leads to the largest enhancement of optical sensitivity but requires an input wavefront that depends on the target position. In sharp contrast, the maximum remission eigenchannel leads to a global enhancement of the sensitivity map with a fixed input wavefront. This global enhancement equals to remission enhancement and preserves the spatial distribution of the sensitivity, making it compatible with existing DOT reconstruction algorithms. Our results establish the theoretical foundation for integrating wavefront control with diffuse optical imaging, enabling deeper tissue penetration through improved signal strength in biomedical applications.

In this note, we elaborate on and explain in detail the proof given by Ziyin et al. (2025) of the "perfect" Platonic Representation Hypothesis (PRH) for the embedded deep linear network model (EDLN). We show that if trained with SGD, two EDLNs with different widths and depths and trained on different data will become Perfectly Platonic, meaning that every possible pair of layers will learn the same representation up to a rotation. Because most of the global minima of the loss function are not Platonic, that SGD only finds the perfectly Platonic solution is rather extraordinary. The proof also suggests at least six ways the PRH can be broken. We also show that in the EDLN model, the emergence of the Platonic representations is due to the same reason as the emergence of progressive sharpening. This implies that these two seemingly unrelated phenomena in deep learning can, surprisingly, have a common cause. Overall, the theory and proof highlight the importance of understanding emergent "entropic forces" due to the irreversibility of SGD training and their role in representation learning. The goal of this note is to be instructive and avoid lengthy technical details.

Strange metal behavior has been observed in an expanding list of quantum materials, with heavy fermion metals serving as a prototype setting. Among the intriguing questions is the nature of charge carriers; there is an increasing recognition that the quasiparticles are lost, as captured by Kondo destruction quantum criticality. Among the recent experimental advances is the measurement of shot noise in a heavy-fermion strange metal. We are thus motivated to study current fluctuations by advancing a minimal Bose-Fermi Kondo lattice model, which admits a well-defined large-$N$ limit. Showing that the model in equilibrium captures the essential physics of Kondo destruction, we proceed to derive quantum kinetic equations and compute shot noise to the leading nontrivial order in $1/N$. Our results reveal a strong suppression of the shot noise at the Kondo destruction quantum critical point, thereby providing the understanding of the striking experiment. Broader implications of our results are discussed.

We investigate how structural ordering, i.e. crystallization, affects the flow of bidisperse granular materials in a quasi-two-dimensional silo. By systematically varying the mass fraction of two particle sizes, we finely tune the degree of local order. Using high-speed imaging and kinematic modeling, we show that crystallization significantly enhances the diffusion length $b$, a key parameter controlling the velocity profiles within the flowing medium. We reveal a strong correlation between $b$ and the hexatic order parameter $\left<|\psi_6|\right>_t$, highlighting the role of local structural organization in governing macroscopic flow behavior. Furthermore, we demonstrate that pressure gradients within the silo promote the stabilization of orientational order even in the absence of crystallization, thus intrinsically increasing $b$ with height. These findings establish a direct link between microstructural order, pressure, and transport properties in granular silo flows.

Understanding the generalization abilities of neural networks for simple input-output distributions is crucial to account for their learning performance on real datasets. The classical teacher-student setting, where a network is trained from data obtained thanks to a label-generating teacher model, serves as a perfect theoretical test bed. In this context, a complete theoretical account of the performance of fully connected one-hidden layer networks in the presence of generic activation functions is lacking. In this work, we develop such a general theory for narrow networks, i.e. networks with a large number of hidden units, yet much smaller than the input dimension. Using methods from statistical physics, we provide closed-form expressions for the typical performance of both finite temperature (Bayesian) and empirical risk minimization estimators, in terms of a small number of weight statistics. In doing so, we highlight the presence of a transition where hidden neurons specialize when the number of samples is sufficiently large and proportional to the number of parameters of the network. Our theory accurately predicts the generalization error of neural networks trained on regression or classification tasks with either noisy full-batch gradient descent (Langevin dynamics) or full-batch gradient descent.