CyberSec Research

Reservoir computing is a powerful framework for real-time information processing, characterized by its high computational ability and quick learning, with applications ranging from machine learning to biological systems. In this paper, we demonstrate that the memory capacity of a reservoir recurrent neural network scales sublinearly with the number of readout neurons. To elucidate this phenomenon, we develop a theoretical framework for analytically deriving memory capacity, attributing the decaying growth of memory capacity to neuronal correlations. In addition, numerical simulations reveal that once memory capacity becomes sublinear, increasing the number of readout neurons successively enables nonlinear processing at progressively higher polynomial orders. Furthermore, our theoretical framework suggests that neuronal correlations govern not only memory capacity but also the sequential growth of nonlinear computational capabilities. Our findings establish a foundation for designing scalable and cost-effective reservoir computing, providing novel insights into the interplay among neuronal correlations, linear memory, and nonlinear processing.

Discrete time crystals (DTC) have emerged as significant phase of matter for out-of-equilibrium many-body systems in recent years. Here, we study the role of long-range interactions and disorder in stabilizing the DTC phase. Generally, it is believed that a stable DTC phase can be realized in disordered systems with short-range interactions. We study the periodically driven quantum Sherrington-Kirkpatrick (SK) model of Ising spin-glass in which all spins are coupled to each other with random couplings. We explore the possibility of DTC phase within three different driving protocols. For all the cases, quantum SK model shows a robust DTC phase with no initial state dependence at all. We compare the periodically driven SK model with other models of long-range interactions with uniform coefficients where randomness is induced through a local field. In complete contrast to the SK model, these models show strong initial state dependence with a large number of initial states showing decay in periodic oscillations in spin-spin correlation function with time.

Markedly increased computational power and data acquisition have led to growing interest in data-driven inverse dynamics problems. These seek to answer a fundamental question: What can we learn from time series measurements of a complex dynamical system? For small systems interacting with external environments, the effective dynamics are inherently stochastic, making it crucial to properly manage noise in data. Here, we explore this for systems obeying Langevin dynamics and, using currents, we construct a learning framework for stochastic modeling. Currents have recently gained increased attention for their role in bounding entropy production (EP) from thermodynamic uncertainty relations (TURs). We introduce a fundamental relationship between the cumulant currents there and standard machine-learning loss functions. Using this, we derive loss functions for several key thermodynamic functions directly from the system dynamics without the (common) intermediate step of deriving a TUR. These loss functions reproduce results derived both from TURs and other methods. More significantly, they open a path to discover new loss functions for previously inaccessible quantities. Notably, this includes access to per-trajectory entropy production, even if the observed system is driven far from its steady-state. We also consider higher order estimation. Our method is straightforward and unifies dynamic inference with recent approaches to entropy production estimation. Taken altogether, this reveals a deep connection between diffusion models in machine learning and entropy production estimation in stochastic thermodynamics.

In order to establish the thermodynamic stability of a system, knowledge of its Gibbs free energy is essential. Most often, the Gibbs free energy is predicted within the CALPHAD framework using models employing thermodynamic properties, such as the mixing enthalpy, heat capacity, and activity coefficients. Here, we present a deep-learning approach capable of predicting the mixing enthalpy of liquid phases of binary systems that were not present in the training dataset. Therefore, our model allows for a system-informed enhancement of the thermodynamic description to unknown binary systems based on information present in the available thermodynamic assessment. Thereby, significant experimental efforts in assessing new systems can be spared. We use an open database for steels containing 91 binary systems to generate our initial training (and validation) and amend it with several direct experimental reports. The model is thoroughly tested using different strategies, including a test of its predictive capabilities. The model shows excellent predictive capabilities outside of the training dataset as soon as some data containing species of the predicted system is included in the training dataset. The estimated uncertainty of the model is below 1 kJ/mol for the predicted mixing enthalpy. Subsequently, we used our model to predict the enthalpy of mixing of all binary systems not present in the original database and extracted the Redlich-Kister parameters, which can be readily reintegrated into the thermodynamic database file.

Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of quantum magnets with neural-network quantum states (NQS), in which the quantum many-body wave function is mapped onto an Ising model. We study the sampling performance of sIM for NQS by comparing sampling on a software-emulated sIM with standard Metropolis-Hastings sampling for NQS. We quantify the sampling efficiency by the number of steps required to reach iso-accurate stochastic estimation of the variational energy and show that this is entirely determined by the autocorrelation time of the sampling. This enables predications of sampling advantage without direct deployment on hardware. For the quantum Heisenberg models studied and experimental results on the runtime of sIMs, we project a possible speed-up of 100 to 10000, suggesting great opportunities for studying complex quantum systems at larger scales.

Quartz is extensively used for luminescence and ESR dosimetry as well as dating. These techniques use inherent defects introduced in quartz crystal during its crystallization in nature. The defect comprises both intrinsic as well as extrinsic defects. These defects give important luminescence properties to quartz but are not yet well understood from a theoretical perspective. Specifically, in case of luminescence dosimetry the nature of traps and their involvement in luminescence production is not exactly known. Thus, present work attempts to understand the basic physics of defects and their implication for luminescence and ESR techniques via Density Functional Theory (DFT) modelling. The work uses DFT to model the presence of some possible major impurities in quartz. Several interesting novel results are obtained that will have implications for ongoing research in Luminescence and ESR methods. The DFT modelling suggested that Oxygen deficiency in quartz crystal results in the formation of both electron and hole trapping centres. However, it is observed that these centres can be passivated by the introduction of charge compensating OH or H ions. Further, it is found that peroxy defects can be formed in the presence of either excess Oxygen or due to the absence of Silicon (Si4+), however, the nature of the traps formed in both cases is different. Besides these intrinsic defects, Al and Fe are the major impurities which are observed as defects in quartz. The modelling of these impurities suggested that negligible change in DOS is observed for Al defect and Fe generally forms a recombination centre or hole trap. In addition to these, there are several interesting first-time observations that are not reported and will be helpful for progressing luminescence and ESR dosimetry research.

This study investigates the quantum effects in transverse-field Ising spin glass models with rotationally invariant random interactions. The primary aim is to evaluate the validity of a quasi-static approximation that captures the imaginary-time dependence of the order parameters beyond the conventional static approximation. Using the replica method combined with the Suzuki--Trotter decomposition, we established a stability condition for the replica symmetric solution, which is analogous to the de Almeida--Thouless criterion. Numerical analysis of the Sherrington--Kirkpatrick model estimates a value of the critical transverse field, $\Gamma_\mathrm{c}$, which agrees with previous Monte Carlo-based estimations. For the Hopfield model, it provides an estimate of $\Gamma_\mathrm{c}$, which has not been previously evaluated. For the random orthogonal model, our analysis suggests that quantum effects alter the random first-order transition scenario in the low-temperature limit. This study supports a quasi-static treatment for analyzing quantum spin glasses and may offer useful insights into the analysis of quantum optimization algorithms.

Non-trivial geometry of electronic Bloch states gives birth to topological insulators that are robust against sufficiently weak randomness, inevitably present in any quantum material. However, increasing disorder triggers a quantum phase transition into a featureless normal insulator. As the underlying quantum critical point is approached from the topological side, small scattered droplets of normal insulators start to develop in the system and their coherent nucleation causes ultimate condensation of a trivial insulation. Unless disorder is too strong, the normal insulator accommodates disjoint tiny topological puddles. Furthermore, in the close vicinity of such a transition the emergent islands of topological and trivial insulators display spatial fractal structures, a feature that is revealed only by local topological markers. Here we showcase this (possibly) generic phenomenon that should be apposite to dirty topological crystals of any symmetry class in any dimension from the Bott index and local Chern marker for a square lattice-based disordered Chern insulator model.

We propose a unifying framework for non-equilibrium relaxation dynamics in ensembles of positionally disordered interacting quantum spins based on the statistical properties, such as mean and variance, of the underlying disorder distribution. Our framework is validated through extensive exact numerical calculations and we use it to disentangle and understand the importance of dimensionality and interaction range for the observation of glassy (i.e., sub-exponential) decay dynamics. Leveraging the deterministic control of qubit positioning enabled by modern tweezer array architectures, we also introduce a method (``J-mapping'') that can be used to emulate the relaxation dynamics of a disordered system with arbitrary dimensionality and interaction range in bespoke one-dimensional arrays. Our approach paves the way towards tunable relaxation dynamics that can be explored in quantum simulators based on arrays of neutral atoms and molecules.

Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy -- known as zero modes -- stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a $U(1)$ particle-conservation symmetry. We use the $U(1)$ East, which lacks inversion symmetry, and the inversion-symmetric $U(1)$ East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a parametric increase in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single particle physics and introduce the notion of collective bound states. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.

Physical risks, such as droughts, floods, rising temperatures, earthquakes, infrastructure failures, and geopolitical conflicts, can ripple through global supply chains, raising costs, and constraining production across industries. Assessing these risks requires understanding not only their immediate effects, but also their cascading impacts. For example, a localized drought can disrupt the supply of critical raw materials such as cobalt or copper, affecting battery and electric vehicle production. Similarly, regional conflicts can impede cross-border trade, leading to broader economic consequences. Building on an existing model of simultaneous supply and demand shocks, we introduce a new propagation algorithm, Priority with Constraint, which modifies standard priority-based rationing by incorporating a minimum supply guarantee for all customers, regardless of their size or priority ranking. We also identify a buffer effect inherent in the Industry Proportional algorithm, which reflects real-world economic resilience. Finally, we extend the static shock propagation model to incorporate dynamic processes. We introduce mechanisms for gradual shock propagation, reflecting demand stickiness and the potential buffering role of inventories, and gradual recovery, modeling the simultaneous recovery of supply capacity and the inherent tendency for demand to return to pre-shock levels. Simulations demonstrate how the interplay between demand adjustment speed and supply recovery speed significantly influences the severity and duration of the economic impact after a shock.

We challenge two foundational principles of localization physics by analyzing conductance fluctuations in two dimensions with unprecedented precision: (i) the Thouless criterion, which defines localization as insensitivity to boundary conditions, and (ii) that symmetry determines the universality class of Anderson localization. We reveal that the fluctuations of the conductance logarithm fall into distinct sub-universality classes inherited from Kardar-Parisi-Zhang (KPZ) physics, dictated by the lead configurations of the scattering system and unaffected by the presence of a magnetic field. Distinguishing between these probability distributions poses a significant challenge due to their striking similarity, requiring sampling beyond the usual threshold of $\sim 10^{-6}$ accessible through independent disorder realizations. To overcome this, we implement an importance sampling scheme - a Monte Carlo approach in disorder space - that enables us to probe rare disorder configurations and sample probability distribution tails down to $10^{-30}$. This unprecedented precision allows us to unambiguously differentiate between KPZ sub-universality classes of conductance fluctuations for different lead configurations, while demonstrating the insensitivity to magnetic fields.

Disordered stealthy hyperuniform (SHU) packings are an emerging class of exotic amorphous two-phase materials endowed with novel physical properties. Such packings of identical spheres have been created from SHU point patterns via a modified collective-coordinate optimization scheme that includes a soft-core repulsion, besides the standard `stealthy' pair potential. Using the distributions of minimum pair distances and nearest-neighbor distances, we find that when the stealthiness parameter $\chi$ is lower than 0.5, the maximal values of $\phi$, denoted by $\phi_{\max}$, decrease to zero on average as the particle number $N$ increases if there are no soft-core repulsions. By contrast, the inclusion of soft-core repulsions results in very large $\phi_{\max}$ independent of $N$, reaching up to $\phi_{\max}=1.0, 0.86, 0.63$ in the zero-$\chi$ limit and decreasing to $\phi_{\max}=1.0, 0.67, 0.47$ at $\chi=0.45$ for $d=1,2,3$, respectively. We obtain explicit formulas for $\phi_{\max}$ as functions of $\chi$ and $N$ for a given $d$. For $d=2,3$, our soft-core SHU packings for small $\chi$ become configurationally very close to the jammed hard-particle packings created by fast compression algorithms, as measured by the pair statistics. As $\chi$ increases beyond $0.20$, the packings form fewer contacts and linear polymer-like chains. The resulting structure factors $S(k)$ and pair correlation functions $g_2(r)$ reveal that soft-core repulsions significantly alter the short- and intermediate-range correlations in the SHU ground states. We also compute the spectral density $\tilde{\chi}_{_V}(k)$, which can be used to estimate various physical properties (e.g., electromagnetic properties, fluid permeability, and mean survival time) of SHU two-phase dispersions. Our results offer a new route for discovering novel disordered hyperuniform two-phase materials with unprecedentedly high density.

Localization of wave functions in the disordered models can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is a smooth function of eigenenergy in the same phase, thus its non-smoothness can serve as strong evidence to determine the phase transition from the extended phase to the localized phase. However, logically, there is no fundamental reason that prohibits this Lyapunov exponent from being non-smooth in the localized phase. In this work, we show that if the localization centers are inhomogeneous in the whole chain and if the system possesses (at least) two different localization modes, the Lyapunov exponent can become non-smooth in the localized phase at the boundaries between the different localization modes. We demonstrate these results using several slowly varying models and show that the singularities of density of states are essential to these non-smoothness, according to the Thouless formula. These results can be generalized to higher-dimensional models, suggesting the possible delicate structures in the localized phase, which can revise our understanding of localization hence greatly advance our comprehension of Anderson localization.

Using functional methods, we investigate in a low-temperature liquid, the sound quanta defined by the quantized hydrodynamic fields, under the effects of high-energy processes on the atomic/molecular scale. To obtain in the molecular level the excitation spectra of liquids, we assume that the quantum fields are coupled to an additive delta-correlated in space and time quantum noise field. The hydrodynamic fields are defined in a fluctuating environment. After defining the generating functional of connected correlation fuctions in the presence of the noise field, we perform a functional integral over all noise field configurations. This is done using a formal object inspired by the distributional zeta-function method, named configurational zeta-function. We obtain a new generating functional written in terms of an analytically tractable functional series. Each term of the series describes in the liquid the emergent non-interacting elementary excitations with the usual gapless phonon-like dispersion relation and additional excitations with dispersion relations with gaps in pseudo-momenta space, i.e., tachyonic-like excitations. Furthermore, the Fourier representation of the two-point correlation functions of the model with the contribution coming from all phononic and tachyonic-like fields is presented. Finally, our analysis reveals that the emergent tachyonic-like and phononic excitations yield a distinctive thermodynamic signature - a quadratic temperature dependence of specific heat ($C_V \propto T^2$) at low temperatures, providing a theoretical foundation for experiments in confined and supercooled liquids.

The electronic density of states (DOS) plays a crucial role in determining the properties of materials. In this study, we investigate the machine learnability of additive atomic contributions to the electronic DOS. Our approach focuses on atom-projected DOS rather than structural DOS. This method for structure-property mapping is both scalable and transferable, achieving high prediction accuracy for pure and compound silicon and carbon structures of varying sizes and configurations. Furthermore, we demonstrate the effectiveness of our method on the complex Sn-S-Se compound structures. By employing locally trained DOS, we significantly enhance the accuracy in predicting secondary material properties, such as band energy, Fermi level, heat capacity, and magnetic susceptibility. Our findings indicate that directly learning atomic DOS, rather than structural DOS, improves the efficiency, accuracy, and interpretability of machine learning in structure-property mapping. This streamlined approach reduces computational complexity, paving the way for the examination of electronic structures in materials without the need for computationally expensive ab initio calculations.

Two nearly universal and anomalous properties of glasses, the peak in the specific heat and plateau of the thermal conductivity, occur around the same temperature. This coincidence suggests that the two phenomena are related. Both effects can be rationalized by assuming Rayleigh scaling of sound attenuation and this scaling leads one to consider scattering from defects. Identifying defects in glasses, which are inherently disordered, is a long-standing problem that was approached in several ways. We examine candidates for defects in glasses that represent areas of strong sound damping. We show that some defects are associated with quasi-localized excitations, which may be associated with modes in excess of the Debye theory. We also examine generalized Debye relations, which relate sound damping and the speed of sound to excess modes. We derive a generalized Debye relation that does not resort to an approximation used by previous authors. We find that our relation and the relation given by previous authors are almost identical at small frequencies and also reproduce the independently determined density of states. However, the different generalized Debye relations do not agree around the boson peak. While generalized Debye relations accurately predict the boson peak in two-dimensional glasses, they under estimate the boson peak in three-dimensional glasses.

While the high-temperature spin diffusion in spin chains with random local fields has been the subject of numerous studies concerning the phenomenon of many-body localization (MBL), the energy diffusion in the same models has been much less explored. We show that energy diffusion is faster at weak random fields but becomes essentially equal at strong fields; hence, both diffusions determine the slowest relaxation time scale (Thouless time) in the system. Numerically reachable finite-size systems reveal the anomalously large distribution of diffusion constants with respect to actual field configurations. Despite the exponential-like dependence of diffusion on field strength, results for the sensitivity to twisted boundary conditions are incompatible with the Thouless criterion for localization and the presumable transition to MBL, at least for numerically reachable sizes. In contrast, we find indications for the scenario of subdiffusive transport, in particular in the dynamical diffusivity response.