arXiv - PHYS - Disordered Systems and Neural Networks最新文献_第9页

Non-Hermitian butterfly spectra in a family of quasiperiodic lattices 准周期晶格族中的非ermitian 蝴蝶谱

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-04-17 DOI: arxiv-2404.11020

Li Wang, Zhenbo Wang, Shu Chen

{"title":"Non-Hermitian butterfly spectra in a family of quasiperiodic lattices","authors":"Li Wang, Zhenbo Wang, Shu Chen","doi":"arxiv-2404.11020","DOIUrl":"https://doi.org/arxiv-2404.11020","url":null,"abstract":"We propose a family of exactly solvable quasiperiodic lattice models with\u0000analytical complex mobility edges, which can incorporate mosaic modulations as\u0000a straightforward generalization. By sweeping a potential tuning parameter\u0000$delta$, we demonstrate a kind of interesting butterfly-like spectra in\u0000complex energy plane, which depicts energy-dependent extended-localized\u0000transitions sharing a common exact non-Hermitian mobility edge. Applying\u0000Avila's global theory, we are able to analytically calculate the Lyapunov\u0000exponents and determine the mobility edges exactly. For the minimal model\u0000without mosaic modulation, a compactly analytic formula for the complex\u0000mobility edges is obtained, which, together with analytical estimation of the\u0000range of complex energy spectrum, gives the true mobility edge. The\u0000non-Hermitian mobility edge in complex energy plane is further verified by\u0000numerical calculations of fractal dimension and spatial distribution of wave\u0000functions. Tuning parameters of non-Hermitian potentials, we also investigate\u0000the variations of the non-Hermitian mobility edges and the corresponding\u0000butterfly spectra, which exhibit richness of spectrum structures.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140610921","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

Heterogeneous mean-field analysis of the generalized Lotka-Volterra model on a network 网络上广义洛特卡-伏特拉模型的异质均场分析

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-04-17 DOI: arxiv-2404.11164

Fabián Aguirre-López

引用次数: 0

Haldane graphene billiards versus relativistic neutrino billiards 霍尔丹石墨烯台球与相对论中微子台球

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-04-11 DOI: arxiv-2404.07679

Dung Xuan Nguyen, Barbara Dietz

{"title":"Haldane graphene billiards versus relativistic neutrino billiards","authors":"Dung Xuan Nguyen, Barbara Dietz","doi":"arxiv-2404.07679","DOIUrl":"https://doi.org/arxiv-2404.07679","url":null,"abstract":"We study fluctuation properties in the energy spectra of finite-size\u0000honeycomb lattices, graphene billiards, subject to the Haldane-model onsite\u0000potential and next-nearest neighbor interaction at critical points, referred to\u0000as Haldane graphene billiards in the following. The billiards had the shapes of\u0000a rectangular billiard with integrable dynamics, one with chaotic dynamics, and\u0000one whose shape has, in addition, threefold rotational symmetry. It had been\u0000shown that the spectral properties of the graphene billiards coincide with\u0000those of the nonrelativistic quantum billiard with the corresponding shape,\u0000both at the band edges and in the region of low energy excitations around the\u0000Dirac points at zero energy. There, the dispersion relation is linear and,\u0000accordingly, the spectrum is described by the same relativistic Dirac equation\u0000for massless half-spin particles as relativistic neutrino billiards, whose\u0000spectral properties agree with those of nonrelativistic quantum billiards with\u0000violated time-reversal invariance. Deviations from the expected behavior are\u0000attributed to differing boundary conditions and backscattering at the boundary,\u0000which leads to a mixing of valley states corresponding to the two Dirac points,\u0000that are mapped into each other through time reversal. We employ a Haldane\u0000model to introduce a gap at one of the two Dirac points so that backscattering\u0000is suppressed in the energy region of the gap and demonstrate that there the\u0000correlations in the spectra comply with those of the neutrino billiard of the\u0000corresponding shape.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140610918","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

A random matrix model for the density of states of jammed soft spheres with applied stress 具有外加应力的卡塞软球状态密度的随机矩阵模型

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-04-10 DOI: arxiv-2404.07064

Mario Pernici

引用次数: 0

Unsupervised machine learning for supercooled liquids 针对过冷液体的无监督机器学习

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-04-06 DOI: arxiv-2404.04473

Yunrui Qiu, Inhyuk Jang, Xuhui Huang, Arun Yethiraj

引用次数: 0

Real-space renormalisation approach to the Chalker-Coddington model revisited: improved statistics 重访查克-科丁顿模型的实空间重正化方法：改进的统计数据

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-03-31 DOI: arxiv-2404.00660

Syl Shaw, Rudolf A. Römer

引用次数: 0

High entropy metallic glasses, what does it mean? 高熵金属眼镜，它意味着什么？

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-03-29 DOI: arxiv-2403.20115

G. V. Afonin, J. C. Qiao, A. S. Makarov, R. A. Konchakov, E. V. Goncharova, N. P. Kobelev, V. A. Khonik

引用次数: 0

Arbitrage equilibrium and the emergence of universal microstructure in deep neural networks 套利均衡与深度神经网络中普遍微观结构的出现

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-03-29 DOI: arxiv-2405.10955

Venkat Venkatasubramanian, N Sanjeevrajan, Manasi Khandekar, Abhishek Sivaram, Collin Szczepanski

{"title":"Arbitrage equilibrium and the emergence of universal microstructure in deep neural networks","authors":"Venkat Venkatasubramanian, N Sanjeevrajan, Manasi Khandekar, Abhishek Sivaram, Collin Szczepanski","doi":"arxiv-2405.10955","DOIUrl":"https://doi.org/arxiv-2405.10955","url":null,"abstract":"Despite the stunning progress recently in large-scale deep neural network\u0000applications, our understanding of their microstructure, 'energy' functions,\u0000and optimal design remains incomplete. Here, we present a new game-theoretic\u0000framework, called statistical teleodynamics, that reveals important insights\u0000into these key properties. The optimally robust design of such networks\u0000inherently involves computational benefit-cost trade-offs that are not\u0000adequately captured by physics-inspired models. These trade-offs occur as\u0000neurons and connections compete to increase their effective utilities under\u0000resource constraints during training. In a fully trained network, this results\u0000in a state of arbitrage equilibrium, where all neurons in a given layer have\u0000the same effective utility, and all connections to a given layer have the same\u0000effective utility. The equilibrium is characterized by the emergence of two\u0000lognormal distributions of connection weights and neuronal output as the\u0000universal microstructure of large deep neural networks. We call such a network\u0000the Jaynes Machine. Our theoretical predictions are shown to be supported by\u0000empirical data from seven large-scale deep neural networks. We also show that\u0000the Hopfield network and the Boltzmann Machine are the same special case of the\u0000Jaynes Machine.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141150761","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

Random Apollonian networks with tailored clustering coefficient 具有定制聚类系数的随机阿波罗网络

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-03-27 DOI: arxiv-2403.18615

Eduardo M. K. Souza, Guilherme M. A. Almeida

引用次数: 0

Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model 非互惠长程奥布里-安德烈-哈珀模型中出现的随强度变化的无标度流动边缘

arXiv - PHYS - Disordered Systems and Neural Networks Pub Date : 2024-03-25 DOI: arxiv-2403.16739

Gui-Juan Liu, Jia-Ming Zhang, Shan-Zhong Li, Zhi Li

引用次数: 0