arxiv_condmatdisnn_bot - Network

This https://arxiv.org/abs/2410.18660 has been replaced. initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113367039463002131link:...

This https://arxiv.org/abs/2410.18660 has been replaced.

initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113367039463002131
link: https://scholar.google.com/scholar?q=arXiv%3A2410.18660

Spectral properties of a disordered insulating lattice under nonlinear electric fieldKunal Mozumdar (University at Buffalo, SUNY, Buffalo,...

Spectral properties of a disordered insulating lattice under nonlinear electric field

Kunal Mozumdar (University at Buffalo, SUNY, Buffalo, NY), Herbert F. Fotso (University at Buffalo, SUNY, Buffalo, NY), Jong E. Han (University at Buffalo, SUNY, Buffalo, NY)
https://arxiv.org/abs/2503.09539 https://arxiv.org/pdf/2503.09539 https://arxiv.org/html/2503.09539

arXiv:2503.09539v1 Announce Type: new
Abstract: Quenched disorder in a solid state system can result in Anderson localization where electrons are exponentially localized and the system behaves like an insulator. In this study, we investigate the effect of a DC electric field on Anderson localization. The study highlights the case of a one-dimensional insulator chain with on-site disorder when a DC electric field is applied throughout the chain. We study spectral properties of an Anderson localized system in equilibrium and out-of-equilibrium using a full lattice nonequilibrium Green's function method in the steady-state limit. Tuning the disorder and the electric field strength results in the creation of exponential Lifshitz tails near the band edge by strongly localized levels. These Lifshtiz tails create effects like insulator-to-metal transitions and contribute to non-local hopping. The electric field causes gradual delocalization of the system and Anderson localization crossing over to Wannier Stark ladders at very strong fields. Our study makes a comparison with the coherent potential approximation (CPA) highlighting some major differences and similarities in the physics of disorder.

The Capacity of Modern Hopfield Networks under the Data Manifold HypothesisBeatrice Achilli, Luca Ambrogioni, Carlo Lucibello, Marc...

The Capacity of Modern Hopfield Networks under the Data Manifold Hypothesis

Beatrice Achilli, Luca Ambrogioni, Carlo Lucibello, Marc M\'ezard, Enrico Ventura
https://arxiv.org/abs/2503.09518 https://arxiv.org/pdf/2503.09518 https://arxiv.org/html/2503.09518

arXiv:2503.09518v1 Announce Type: new
Abstract: We generalize the computation of the capacity of exponential Hopfield model from Lucibello and M\'ezard (2024) to more generic pattern ensembles, including binary patterns and patterns generated from a hidden manifold model.

Effective conductivity of conduit networks with random conductivitiesI. Colecchio, E. Le Gall, B. Noetingerhttps://arxiv.org/abs/2503.09457...

Effective conductivity of conduit networks with random conductivities

I. Colecchio, E. Le Gall, B. Noetinger
https://arxiv.org/abs/2503.09457 https://arxiv.org/pdf/2503.09457 https://arxiv.org/html/2503.09457

arXiv:2503.09457v1 Announce Type: new
Abstract: The effective conductivity ($T^{eff}$) of 2D and 3D Random Resistor Networks (RRNs) with random edge conductivity is studied. The combined influence of geometrical disorder, which controls the overall connectivity of the medium and leads to percolation effects, and conductivity randomness is investigated. A formula incorporating connectivity aspects and second-order averaging methods, widely used in the stochastic hydrology community, is derived and extrapolated to higher orders using a power averaging formula based on a mean-field argument. This approach highlights the role of the so-called resistance distance introduced by graph theorists. Simulations are performed on various RRN geometries constructed from 2D and 3D bond-percolation lattices. The results confirm the robustness of the power averaging technique and the relevance of the mean-field assumption.

Graph-Dynamics correspondence in metallic glass-forming liquidsXin-Jia Zhou, Feng Yang, Xiao-Dong Yang, Lin Ma, Zhen-Wei...

Graph-Dynamics correspondence in metallic glass-forming liquids

Xin-Jia Zhou, Feng Yang, Xiao-Dong Yang, Lin Ma, Zhen-Wei Wu
https://arxiv.org/abs/2503.09278 https://arxiv.org/pdf/2503.09278 https://arxiv.org/html/2503.09278

arXiv:2503.09278v1 Announce Type: new
Abstract: Theoretical challenges in understanding the nature of glass and the glass transition remain significant open questions in statistical and condensed matter physics. As a prototypical example of complex physical systems, glasses and the vitrification process have been central research topics, consistently attracting broad scientific interest. This focus has driven extensive studies on phenomena such as aging, non-exponential relaxation, dynamic anomalies, glass-forming ability, and the mechanical response of glasses under stress. Recent advances in computational and experimental techniques have enabled rigorous testing of theoretical models, shedding new light on glassy behavior. However, the intrinsic complexity of glass and the glass transition that lies in their physics, which spans multiple length and time scales, makes the system challenging to characterize. In this review, we emphasize the need to move beyond conventional approaches and propose a topological perspective as a promising alternative to address these challenges. Specifically, our findings reveal that the diversity in particle relaxation behavior is statistically linked to a global topological feature of the transient network structures formed by the particles in a given liquid. This direction offers opportunities to uncover novel phenomena that could fundamentally reshape our understanding of glassy materials.

Power-law banded random matrix ensemble as a model for quantum many-body HamiltoniansWouter Buijsman, Masudul Haque, Ivan M....

Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians

Wouter Buijsman, Masudul Haque, Ivan M. Khaymovich
https://arxiv.org/abs/2503.08825 https://arxiv.org/pdf/2503.08825 https://arxiv.org/html/2503.08825

arXiv:2503.08825v1 Announce Type: new
Abstract: Hamiltonians of one-dimensional, disordered single-particle systems with long-range hopping terms can naturally be modeled by power-law banded random matrices. In this picture, the phase diagram of a power-law banded random matrix ensemble show ergodic, weakly ergodic, multifractal, and localized phases. Motivated by recent developments on ergodicity breaking and localization in interacting quantum many-body systems, we explore many-body interpretations of the power-law banded random matrix ensemble. We discuss a number of ways to label the basis vectors with many-body configurations, and compare the physical properties of the resulting Hamiltonians. We characterize the scaling of the many-body eigenstate entanglement entropy with system size for the different labeling schemes and in each of the phases. Using a scaling analysis on the full sets of eigenstates, we subsequently provide a quantitative picture of the boundary between the different types of scaling behavior that we observe for the spectral-bulk and spectral-edge eigenstates.

[2025-03-13 Thu (UTC), 5 new articles found for cond-mat.dis-nn Disordered Systems and Neural Networks]

[2025-03-13 Thu (UTC), 5 new articles found for cond-mat.dis-nn Disordered Systems and Neural Networks]

This https://arxiv.org/abs/2502.08192 has been replaced. initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113995323776065591link:...

This https://arxiv.org/abs/2502.08192 has been replaced.

initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113995323776065591
link: https://scholar.google.com/scholar?q=arXiv%3A2502.08192

This https://arxiv.org/abs/2410.18010 has been replaced. initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113361437768591679link:...

This https://arxiv.org/abs/2410.18010 has been replaced.

initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113361437768591679
link: https://scholar.google.com/scholar?q=arXiv%3A2410.18010

This https://arxiv.org/abs/2409.12781 has been replaced. initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113168863087825861link:...

This https://arxiv.org/abs/2409.12781 has been replaced.

initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/113168863087825861
link: https://scholar.google.com/scholar?q=arXiv%3A2409.12781

This https://arxiv.org/abs/2406.12677 has been replaced. initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/112642117230459898link:...

This https://arxiv.org/abs/2406.12677 has been replaced.

initial toot: https://mastoxiv.page/@arXiv_condmatdisnn_bot/112642117230459898
link: https://scholar.google.com/scholar?q=arXiv%3A2406.12677

Sampling the space of solutions of an artificial neural networkAlessandro Zambon, Enrico M. Malatesta, Guido Tiana, Riccardo...

Sampling the space of solutions of an artificial neural network

Alessandro Zambon, Enrico M. Malatesta, Guido Tiana, Riccardo Zecchina
https://arxiv.org/abs/2503.08266 https://arxiv.org/pdf/2503.08266 https://arxiv.org/html/2503.08266

arXiv:2503.08266v1 Announce Type: new
Abstract: The weight space of an artificial neural network can be systematically explored using tools from statistical mechanics. We employ a combination of a hybrid Monte Carlo algorithm which performs long exploration steps, a ratchet-based algorithm to investigate connectivity paths, and coupled replica models simulations to study subdominant flat regions. Our analysis focuses on one hidden layer networks and spans a range of energy levels and constrained density regimes. Near the interpolation threshold, the low-energy manifold shows a spiky topology. While these spikes aid gradient descent, they can trap general sampling algorithms at low temperatures; they remain connected by complex paths in a confined, non-flat region. In the overparameterized regime, however, the low-energy manifold becomes entirely flat, forming an extended complex structure that is easy to sample. These numerical results are supported by an analytical study of the training error landscape, and we show numerically that the qualitative features of the loss landscape are robust across different data structures. Our study aims to provide new methodological insights for developing scalable methods for large networks.

Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement MeasuresMohammad...

Directional Localization in Disordered 2D Tight-Binding Systems: Insights from Single Particle Entanglement Measures

Mohammad Pouranvari
https://arxiv.org/abs/2503.08194 https://arxiv.org/pdf/2503.08194 https://arxiv.org/html/2503.08194

arXiv:2503.08194v1 Announce Type: new
Abstract: We investigate the directional localization properties of wave-functions in a two-dimensional tight-binding model with uniform hopping and correlated random on-site energies. By controlling the disorder correlation strength with a parameter $\alpha$, we explore the effects of disorder on wave-function localization using Single Particle Entanglement Entropy (SPEE) and Single Particle R\'enyi Entropy (SPRE) at different values of $q$. Our analysis includes two distinct randomness structures: row-wise and fully correlated disorder. We find that row-wise disorder maintains maximal entanglement for horizontal cuts while enhancing horizontal spread for vertical cuts as $\alpha$ increases. In contrast, fully correlated disorder leads to reduced vertical entanglement for horizontal cuts and increased horizontal entanglement for vertical cuts with rising $\alpha$. Additionally, our results show that the difference between SPEE and SPRE provides valuable insights into localization behavior. These findings highlight the significance of directional properties in understanding localization transitions in disordered systems.

Phase Transitions and Critical Behavior in Quasi-One-Dimensional Two-Channel Systems with Quasiperiodic DisorderMohammad...

Phase Transitions and Critical Behavior in Quasi-One-Dimensional Two-Channel Systems with Quasiperiodic Disorder

Mohammad Pouranvari
https://arxiv.org/abs/2503.08143 https://arxiv.org/pdf/2503.08143 https://arxiv.org/html/2503.08143

arXiv:2503.08143v1 Announce Type: new
Abstract: We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-Andr\'{e} model. By analyzing the Lyapunov exponent and localization length, we characterize the phase transitions and critical behavior of the system. For the symmetric model, we obtain the phase diagram for the entire spectrum, revealing mobility edges between delocalized and localized states. In contrast, for the asymmetric model, we identify a critical line $ \lambda_1^c + \lambda_2^c \approx 0.5 $ marking the phase transition between delocalized and localized states. We also study the effects of the inter-channel coupling $ \tilde{t} $, and observe that increasing $ \tilde{t} $ reduces the delocalized phase space, shifting the transition from $ \lambda_1 = \lambda_2 = 1 $ at $ \tilde{t} = 0 $ to $ \lambda_1^c + \lambda_2^c \approx 0.5 $ at larger $ \tilde{t} $. Furthermore, the phase transition point is found to be sensitive to both $ \tilde{t} $ and the incommensurate modulation parameter $ b $. While the general phase transition behavior is preserved, subtle differences arise for different values of $ b $, indicating a dependence of the phase boundary on both parameters. Using the cost function approach, we calculate the critical potential strength $ \lambda_c $ and the critical exponent $ \nu $, with $ \nu \approx 0.5 $ for the middle of the spectrum in both symmetric and asymmetric models.

Topological mechanical neural networks as classifiers through in situ backpropagation learningShuaifeng Li, Xiaoming...

Topological mechanical neural networks as classifiers through in situ backpropagation learning

Shuaifeng Li, Xiaoming Mao
https://arxiv.org/abs/2503.07796 https://arxiv.org/pdf/2503.07796 https://arxiv.org/html/2503.07796

arXiv:2503.07796v1 Announce Type: new
Abstract: Recently, a new frontier in computing has emerged with physical neural networks(PNNs) harnessing intrinsic physical processes for learning. Here, we explore topological mechanical neural networks(TMNNs) inspired by the quantum spin Hall effect(QSHE) in topological metamaterials, for machine learning classification tasks. TMNNs utilize pseudospin states and the robustness of the QSHE, making them damage-tolerant for binary classification. We first demonstrate data clustering using untrained TMNNs. Then, for specific tasks, we derive an in situ backpropagation algorithm - a two-step, local-rule method that updates TMNNs using only local information, enabling in situ physical learning. TMNNs achieve high accuracy in classifications of Iris flowers, Penguins, and Seeds while maintaining robustness against bond pruning. Furthermore, we demonstrate parallel classification via frequency-division multiplexing, assigning different tasks to distinct frequencies for enhanced efficiency. Our work introduces in situ backpropagation for wave-based mechanical neural networks and positions TMNNs as promising neuromorphic computing hardware for classification tasks.

Effect of imaginary gauge on wave transport in driven-dissipative systemsI. Komis, K. G. Makris, K. Busch, R....

Effect of imaginary gauge on wave transport in driven-dissipative systems

I. Komis, K. G. Makris, K. Busch, R. El-Ganainy
https://arxiv.org/abs/2503.07786 https://arxiv.org/pdf/2503.07786 https://arxiv.org/html/2503.07786

arXiv:2503.07786v1 Announce Type: new
Abstract: Wave transport in disordered media is a fundamental problem with direct implications in condensed matter, materials science, optics, atomic physics, and even biology. The majority of studies are focused on Hermitian systems to understand disorder-induced localization. However, recent studies of non-Hermitian disordered media have revealed unique behaviors, with a universal principle emerging that links the eigenvalue spectrum of the disordered Hamiltonian and its statistics with its transport properties. In this work we show that the situation can be very different in driven-dissipative lattices of cavities, where a uniform gain applied equally to all the components of the system can act as a knob for controlling the wave transport properties without altering the eigenvalue statistics of the underlying Hamiltonian. Our results open a new avenue for developing a deeper insight into the transport properties in disordered media and will aid in building new devices as well. Our work which is presented in the context of optics generalizes to any physical platforms where gain can be implemented. These include acoustics, electronics, and coupled quantum oscillators such as atoms, diamond centers and superconducting qubits.

Geometric Delocalization in Two DimensionsLaura Shou, Alireza Parhizkar, Victor Galitskihttps://arxiv.org/abs/2503.07705...

Geometric Delocalization in Two Dimensions

Laura Shou, Alireza Parhizkar, Victor Galitski
https://arxiv.org/abs/2503.07705 https://arxiv.org/pdf/2503.07705 https://arxiv.org/html/2503.07705

arXiv:2503.07705v1 Announce Type: new
Abstract: We demonstrate the existence of transient two-dimensional surfaces where a random-walking particle escapes to infinity in contrast to localization in standard flat 2D space. We first prove that any rotationally symmetric 2D membrane embedded in flat 3D space cannot be transient. Then we formulate a criterion for the transience of a general asymmetric 2D membrane. We use it to explicitly construct a class of transient 2D manifolds with a non-trivial metric and height function but ``zero average curvature,'' which we dub tablecloth manifolds. The absence of the logarithmic infrared divergence of the Laplace-Beltrami operator in turn implies the absence of weak localization, non-existence of bound states in shallow potentials, and breakdown of the Mermin-Wagner theorem and Kosterlitz-Thouless transition on the tablecloth manifolds, which may be realizable in both quantum simulators and corrugated two-dimensional materials.

[2025-03-12 Wed (UTC), 6 new articles found for cond-mat.dis-nn Disordered Systems and Neural Networks]

[2025-03-12 Wed (UTC), 6 new articles found for cond-mat.dis-nn Disordered Systems and Neural Networks]

Multi-channel pattern reconstruction through $L$-directional associative memoriesElena Agliari, Andrea Alessandrelli, Paulo Duarte Mourao,...

Multi-channel pattern reconstruction through $L$-directional associative memories

Elena Agliari, Andrea Alessandrelli, Paulo Duarte Mourao, Alberto Fachechi
https://arxiv.org/abs/2503.06274 https://arxiv.org/pdf/2503.06274 https://arxiv.org/html/2503.06274

arXiv:2503.06274v1 Announce Type: new
Abstract: We consider $L$-directional associative memories, composed of $L$ Hopfield networks, displaying imitative Hebbian intra-network interactions and anti-imitative Hebbian inter-network interactions, where couplings are built over a set of hidden binary patterns. We evaluate the model's performance in reconstructing the whole set of hidden binary patterns when provided with mixtures of noisy versions of these patterns. Our numerical results demonstrate the model's high effectiveness in the reconstruction task for structureless and structured datasets.

Scaling laws of shrinkage induced fragmentation phenomenaRoland Szatm\'ari, Akio Nakahara, So Kitsunezaki, Ferenc...

Scaling laws of shrinkage induced fragmentation phenomena

Roland Szatm\'ari, Akio Nakahara, So Kitsunezaki, Ferenc Kun
https://arxiv.org/abs/2503.06177 https://arxiv.org/pdf/2503.06177 https://arxiv.org/html/2503.06177

arXiv:2503.06177v1 Announce Type: new
Abstract: We investigate the shrinkage induced breakup of thin layers of heterogeneous materials attached to a substrate, a ubiquitous natural phenomenon with a wide range of potential applications. Focusing on the evolution of the fragment ensemble, we demonstrate that the system has two distinct phases: damage phase, where the layer is cracked, however, a dominant piece persists retaining the structural integrity of the layer, and a fragmentation phase, where the layer disintegrates into numerous small pieces. Based on finite size scaling we show that the transition between the two phases occurs at a critical damage analogous to continuous phase transitions. At the critical point a fully connected crack network emerges whose structure is controlled by the strength of adhesion to the substrate. In the strong adhesion limit, damage arises from random microcrack nucleation, resembling bond percolation, while weak adhesion facilitates stress concentration and the growth of cracks to large extensions. The critical exponents of the damage to fragmentation transition agree to a reasonable accuracy with those of the two-dimensional Ising model. Our findings provide a novel insights into the mechanism of shrinkage-induced cracking revealing generic scaling laws of the phenomenon.