arXiv - PHYS - Disordered Systems and Neural Networks最新文献

Fast Analysis of the OpenAI O1-Preview Model in Solving Random K-SAT Problem: Does the LLM Solve the Problem Itself or Call an External SAT Solver? 快速分析 OpenAI O1-Preview 模型在解决随机 K-SAT 问题中的作用：LLM 是自己解决问题还是调用外部 SAT 解算器？

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-17 DOI: arxiv-2409.11232

Raffaele Marino

引用次数: 0

Trade-off relations between quantum coherence and measure of many-body localization 量子相干性与多体定位测量之间的权衡关系

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-16 DOI: arxiv-2409.10449

Arti Garg, Arun Kumar Pati

{"title":"Trade-off relations between quantum coherence and measure of many-body localization","authors":"Arti Garg, Arun Kumar Pati","doi":"arxiv-2409.10449","DOIUrl":"https://doi.org/arxiv-2409.10449","url":null,"abstract":"Quantum coherence, a fundamental resource in quantum computing and quantum\u0000information, often competes with localization effects that affects quantum\u0000states in disordered systems. In this work, we prove exact trade-off relations\u0000between quantum coherence and a measure of localization and many-body\u0000localization, namely, the inverse participation ratio (IPR). We prove that the\u0000l1-norm of quantum coherence and the relative entropy of coherence for a pure\u0000quantum state satisfy complementarity relations with IPR. For a mixed state,\u0000IPR and the l2-norm of quantum coherence as well as relative entropy of\u0000coherence satisfy trade-off inequalities. These relations suggest that quantum\u0000coherence, in disordered quantum systems is also an ideal characterization of\u0000the delocalisation to many-body localisation transition, much like IPR, which\u0000is a well-known diagnostic of MBL. These relations also provide insight into\u0000the unusual properties of bipartite entanglement entropy across the MBL\u0000transition. We believe that these trade-off relations can help in better\u0000understanding of how coherence can be preserved or lost in realistic many-body\u0000quantum systems, which is vital for developing robust quantum technologies and\u0000uncovering new phases of quantum matter.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Soft modes in vector spin glass models on sparse random graphs 稀疏随机图上矢量自旋玻璃模型中的软模式

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-16 DOI: arxiv-2409.10312

Silvio Franz, Cosimo Lupo, Flavio Nicoletti, Giorgio Parisi, Federico Ricci-Tersenghi

{"title":"Soft modes in vector spin glass models on sparse random graphs","authors":"Silvio Franz, Cosimo Lupo, Flavio Nicoletti, Giorgio Parisi, Federico Ricci-Tersenghi","doi":"arxiv-2409.10312","DOIUrl":"https://doi.org/arxiv-2409.10312","url":null,"abstract":"We study numerically the Hessian of low-lying minima of vector spin glass\u0000models defined on random regular graphs. We consider the two-component (XY) and\u0000three-component (Heisenberg) spin glasses at zero temperature, subjected to the\u0000action of a randomly oriented external field. Varying the intensity of the\u0000external field, these models undergo a zero temperature phase transition from a\u0000paramagnet at high field to a spin glass at low field. We study how the\u0000spectral properties of the Hessian depend on the magnetic field. In particular,\u0000we study the shape of the spectrum at low frequency and the localization\u0000properties of low energy eigenvectors across the transition. We find that in\u0000both phases the edge of the spectral density behaves as $lambda^{3/2}$: such a\u0000behavior rules out the presence of a diverging spin-glass susceptibility\u0000$chi_{SG}=langle 1/lambda^2 rangle$. As to low energy eigenvectors, we find\u0000that the softest eigenmodes are always localized in both phases of the two\u0000models. However, by studying in detail the geometry of low energy eigenmodes\u0000across different energy scales close to the lower edge of the spectrum, we find\u0000a different behavior for the two models at the transition: in the XY case, low\u0000energy modes are typically localized; at variance, in the Heisenberg case\u0000low-energy eigenmodes with a multi-modal structure (sort of ``delocalization'')\u0000appear at an energy scale that vanishes in the infinite size limit. These\u0000geometrically non-trivial excitations, which we call Concentrated and\u0000Delocalised Low Energy Modes (CDLEM), coexist with trivially localised\u0000excitations: we interpret their existence as a sign of critical behavior\u0000related to the onset of the spin glass phase.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Boolean mean field spin glass model: rigorous results 布尔均场自旋玻璃模型：严格的结果

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-13 DOI: arxiv-2409.08693

Linda Albanese, Andrea Alessandrelli

{"title":"Boolean mean field spin glass model: rigorous results","authors":"Linda Albanese, Andrea Alessandrelli","doi":"arxiv-2409.08693","DOIUrl":"https://doi.org/arxiv-2409.08693","url":null,"abstract":"Spin glasses have played a fundamental role in statistical mechanics field.\u0000Purpose of this work is to analyze a variation on theme of the mean field case\u0000of them, when the Ising spins are replaced to Boolean ones, i.e. {0,1} possible\u0000values. This may be useful to continue building a solid bridge between statical\u0000mechanics of spin glasses and Machine Learning techniques. We have drawn a\u0000detailed framework of this model: we have applied Guerra and Toninelli's\u0000approach to prove the existence of the thermodynamic quenched statistical\u0000pressure for this model recovering its expression using Guerra's interpolation.\u0000Specifically, we have supposed Replica Symmetric assumption and first step of\u0000Replica Symmetry Breaking approximation for the probability distribution of the\u0000order parameter of the model. Then, we analyze the stability of the resolution\u0000in both assumptions via de Almeida-Thouless line, proving that the Replica\u0000Symmetric one well describes the model apart for small values of temperature,\u0000when the Replica Symmetry Breaking is better. All the theoretical parts are\u0000supported by numerical techniques that demonstrate perfect consistency with the\u0000analytical results.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142253823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized hetero-associative neural networks 广义异质关联神经网络

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-12 DOI: arxiv-2409.08151

Elena Agliari, Andrea Alessandrelli, Adriano Barra, Martino Salomone Centonze, Federico Ricci-Tersenghi

{"title":"Generalized hetero-associative neural networks","authors":"Elena Agliari, Andrea Alessandrelli, Adriano Barra, Martino Salomone Centonze, Federico Ricci-Tersenghi","doi":"arxiv-2409.08151","DOIUrl":"https://doi.org/arxiv-2409.08151","url":null,"abstract":"While auto-associative neural networks (e.g., the Hopfield model implementing\u0000the standard Hebbian prescription for learning) play as the reference setting\u0000for pattern recognition and associative memory in statistical mechanics,\u0000hetero-associative extensions (despite much less investigated) display richer\u0000emergent computational skills. Here we study the simplest generalization of the\u0000Kosko's Bidirectional Associative Memory (BAM), namely a Three-directional\u0000Associative Memory (TAM), that is a tripartite neural network equipped with\u0000generalized Hebbian weights. We study its information processing capabilities\u0000analytically (via statistical mechanics and signal-to-noise techniques) and\u0000computationally (via Monte Carlo simulations). Confined to the replica\u0000symmetric description, we provide phase diagrams for this network in the space\u0000of the control parameters, highlighting the existence of a region where the\u0000machine can successful perform recognition as well as other tasks. For\u0000instance, it can perform pattern disentanglement, namely when inputted with a\u0000mixture of patterns, the network is able to return the original patterns,\u0000namely to disentangle the signal's components. Further, they can also perform\u0000retrieval of (Markovian) sequences of patterns and they can also disentangle\u0000mixtures of periodic patterns: should these mixtures be sequences that combine\u0000patterns alternating at different frequencies, these hetero-associative\u0000networks can perform generalized frequency modulation by using the slowly\u0000variable sequence of patterns as the base-band signal and the fast one as the\u0000information carrier.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach 经典和量子洛伦兹模型中的扩散、长尾和定位：统一的流体力学方法

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-12 DOI: arxiv-2409.08123

T. R. Kirkpatrick, D. Belitz

引用次数: 0

Numerical study of Darcy's law of yield stress fluids on a deep tree-like network 深层树状网络上屈服应力流体的达西定律数值研究

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-05 DOI: arxiv-2409.03480

Stéphane Munier, Alberto Rosso

引用次数: 0

Exact anomalous mobility edges in one-dimensional non-Hermitian quasicrystals 一维非赫米提准晶体中的精确反常迁移率边缘

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-05 DOI: arxiv-2409.03591

Xiang-Ping Jiang, Weilei Zeng, Yayun Hu, Lei Pan

{"title":"Exact anomalous mobility edges in one-dimensional non-Hermitian quasicrystals","authors":"Xiang-Ping Jiang, Weilei Zeng, Yayun Hu, Lei Pan","doi":"arxiv-2409.03591","DOIUrl":"https://doi.org/arxiv-2409.03591","url":null,"abstract":"Recent research has made significant progress in understanding localization\u0000transitions and mobility edges (MEs) that separate extended and localized\u0000states in non-Hermitian (NH) quasicrystals. Here we focus on studying critical\u0000states and anomalous MEs, which identify the boundaries between critical and\u0000localized states within two distinct NH quasiperiodic models. Specifically, the\u0000first model is a quasiperiodic mosaic lattice with both nonreciprocal hopping\u0000term and on-site potential. In contrast, the second model features an unbounded\u0000quasiperiodic on-site potential and nonreciprocal hopping. Using Avila's global\u0000theory, we analytically derive the Lyapunov exponent and exact anomalous MEs.\u0000To confirm the emergence of the robust critical states in both models, we\u0000conduct a numerical multifractal analysis of the wave functions and spectrum\u0000analysis of level spacing. Furthermore, we investigate the transition between\u0000real and complex spectra and the topological origins of the anomalous MEs. Our\u0000results may shed light on exploring the critical states and anomalous MEs in NH\u0000quasiperiodic systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Machine learning of phases and structures for model systems in physics 物理学模型系统相位和结构的机器学习

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-04 DOI: arxiv-2409.03023

Djenabou Bayo, Burak Çivitcioğlu, Joseph J Webb, Andreas Honecker, Rudolf A. Römer

引用次数: 0

Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures 具有异质温度的 Ornstein-Uhlenbeck 过程协方差矩阵的随机矩阵集合

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-09-02 DOI: arxiv-2409.01262

Leonardo Ferreira, Fernando Metz, Paolo Barucca

{"title":"Random matrix ensemble for the covariance matrix of Ornstein-Uhlenbeck processes with heterogeneous temperatures","authors":"Leonardo Ferreira, Fernando Metz, Paolo Barucca","doi":"arxiv-2409.01262","DOIUrl":"https://doi.org/arxiv-2409.01262","url":null,"abstract":"We introduce a random matrix model for the stationary covariance of\u0000multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures,\u0000where the covariance is constrained by the Sylvester-Lyapunov equation. Using\u0000the replica method, we compute the spectral density of the equal-time\u0000covariance matrix characterizing the stationary states, demonstrating that this\u0000model undergoes a transition between stable and unstable states. In the stable\u0000regime, the spectral density has a finite and positive support, whereas\u0000negative eigenvalues emerge in the unstable regime. We determine the critical\u0000line separating these regimes and show that the spectral density exhibits a\u0000power-law tail at marginal stability, with an exponent independent of the\u0000temperature distribution. Additionally, we compute the spectral density of the\u0000lagged covariance matrix characterizing the stationary states of linear\u0000transformations of the original dynamical variables. Our random-matrix model is\u0000potentially interesting to understand the spectral properties of empirical\u0000correlation matrices appearing in the study of complex systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0