arXiv: Disordered Systems and Neural Networks最新文献_第10页

Detecting a many-body mobility edge with quantum quenches 用量子猝灭检测多体迁移率边缘

arXiv: Disordered Systems and Neural Networks Pub Date : 2016-07-05 DOI: 10.21468/SciPostPhys.1.1.010

P. Naldesi, E. Ercolessi, T. Roscilde

{"title":"Detecting a many-body mobility edge with quantum quenches","authors":"P. Naldesi, E. Ercolessi, T. Roscilde","doi":"10.21468/SciPostPhys.1.1.010","DOIUrl":"https://doi.org/10.21468/SciPostPhys.1.1.010","url":null,"abstract":"The many-body localization (MBL) transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from \"extended/ergodic\" (exhibiting extensive entanglement entropies and fluctuations) to \"localized\" (exhibiting area-law scaling of entanglement and fluctuations). The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using \"quantum-quench spectroscopy\", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81465182","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: 43

Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions 玻璃和干扰过渡:从精确结果到有限维描述

arXiv: Disordered Systems and Neural Networks Pub Date : 2016-05-10 DOI: 10.1146/annurev-conmatphys-031016-025334

P. Charbonneau, J. Kurchan, G. Parisi, P. Urbani, F. Zamponi

引用次数: 244

Statistical mechanical models of integer factorization problem 整数分解问题的统计力学模型

arXiv: Disordered Systems and Neural Networks Pub Date : 2016-05-04 DOI: 10.7566/JPSJ.86.014001

C. Nakajima, Masayuki Ohzeki

引用次数: 0

Grand Projection State: A Single Microscopic State to Determine Free Energy 大投射态:决定自由能的单一微观态

arXiv: Disordered Systems and Neural Networks Pub Date : 2016-04-20 DOI: 10.7566/JPSJ.86.114802

Tetsuya Taikei, T. Kishimoto, Kazuhito Takeuchi, Koretaka Yuge

引用次数: 0

Criticality and Energy Landscapes in Spin Glasses 自旋玻璃中的临界性和能量景观

arXiv: Disordered Systems and Neural Networks Pub Date : 2016-02-26 DOI: 10.1007/978-3-319-41231-3

M. Baity-Jesi

引用次数: 4

Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals 无序三维Dirac和Weyl半金属的稀有区诱导避免量子临界

arXiv: Disordered Systems and Neural Networks Pub Date : 2016-02-08 DOI: 10.1103/PhysRevX.6.021042

J. Pixley, D. Huse, S. Sarma

{"title":"Rare region induced avoided quantum criticality in disordered three-dimensional Dirac and Weyl semimetals","authors":"J. Pixley, D. Huse, S. Sarma","doi":"10.1103/PhysRevX.6.021042","DOIUrl":"https://doi.org/10.1103/PhysRevX.6.021042","url":null,"abstract":"We numerically study the effect of short ranged potential disorder on massless noninteracting three-dimensional Dirac and Weyl fermions, with a focus on the question of the proposed quantum critical point separating the semimetal and diffusive metal phases. We determine the properties of the eigenstates of the disordered Dirac Hamiltonian ($H$) and exactly calculate the density of states (DOS) near zero energy, using a combination of Lanczos on $H^2$ and the kernel polynomial method on $H$. We establish the existence of two distinct types of low energy eigenstates contributing to the disordered density of states in the weak disorder semimetal regime. These are (i) typical eigenstates that are well described by linearly dispersing perturbatively dressed Dirac states, and (ii) nonperturbative rare eigenstates that are weakly-dispersive and quasi-localized in the real space regions with the largest (and rarest) local random potential. Using twisted boundary conditions, we are able to systematically find and study these two types of eigenstates. We find that the Dirac states contribute low energy peaks in the finite-size DOS that arise from the clean eigenstates which shift and broaden in the presence of disorder. On the other hand, we establish that the rare quasi-localized eigenstates contribute a nonzero background DOS which is only weakly energy-dependent near zero energy and is exponentially small at weak disorder. We find that the expected semimetal to diffusive metal quantum critical point is converted to an {it avoided} quantum criticality that is \"rounded out\" by nonperturbative effects, with no signs of any singular behavior in the DOS near the Dirac energy. We discuss the implications of our results for disordered Dirac and Weyl semimetals, and reconcile the large body of existing numerical work showing quantum criticality with the existence of the rare region effects.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81849369","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: 52

Theoretical study on density of microscopic states in configuration space via Random Matrix 构形空间中微观态密度的随机矩阵理论研究

arXiv: Disordered Systems and Neural Networks Pub Date : 2015-11-26 DOI: 10.14723/TMRSJ.41.213

Koretaka Yuge, Kazuhito Takeuchi, Tetuya Kishimoto

{"title":"Theoretical study on density of microscopic states in configuration space via Random Matrix","authors":"Koretaka Yuge, Kazuhito Takeuchi, Tetuya Kishimoto","doi":"10.14723/TMRSJ.41.213","DOIUrl":"https://doi.org/10.14723/TMRSJ.41.213","url":null,"abstract":"In classical systems, our recent theoretical study provides new insight into how spatial constraint on the system connects with macroscopic properties, which lead to universal representation of equilibrium macroscopic physical property and structure in disordered states. These important characteristics rely on the fact that statistical interdependence for density of microscopic states (DOMS) in configuration space appears numerically vanished at thermodynamic limit for a wide class of spatial constraints, while such behavior of the DOMS is not quantitatively well-understood so far. The present study theoretically address this problem based on the Random Matrix with Gaussian Orthogonal Ensemble, where corresponding statistical independence is mathematically guaranteed. Using the generalized Ising model, we confirm that lower-order moment of density of eigenstates (DOE) of covariance matrix of DOMS shows asymptotic behavior to those for Random Matrix with increase of system size. This result supports our developed theoretical approach, where equilibrium macroscopic property in disordered states can be decomposed into individual contribtion from each generalized coordinate with the sufficiently high number of constituents in the given system, leading to representing equilibrium macroscopic properties by a few special microscopic states.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78461061","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: 3

Transition to chaos in random neuronal networks 随机神经网络向混沌的过渡

arXiv: Disordered Systems and Neural Networks Pub Date : 2015-08-26 DOI: 10.1103/PhysRevX.5.041030

Jonathan Kadmon, H. Sompolinsky

{"title":"Transition to chaos in random neuronal networks","authors":"Jonathan Kadmon, H. Sompolinsky","doi":"10.1103/PhysRevX.5.041030","DOIUrl":"https://doi.org/10.1103/PhysRevX.5.041030","url":null,"abstract":"Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic dynamics. Indeed, simplified rate-based large neuronal networks with random synaptic connections are known to exhibit sharp transition from fixed point to chaotic dynamics when the synaptic gain is increased. However, the existence of a similar transition in neuronal circuit models with more realistic architectures and firing dynamics has not been established. \u0000In this work we investigate rate based dynamics of neuronal circuits composed of several subpopulations and random connectivity. Nonzero connections are either positive-for excitatory neurons, or negative for inhibitory ones, while single neuron output is strictly positive; in line with known constraints in many biological systems. Using Dynamic Mean Field Theory, we find the phase diagram depicting the regimes of stable fixed point, unstable dynamic and chaotic rate fluctuations. We characterize the properties of systems near the chaotic transition and show that dilute excitatory-inhibitory architectures exhibit the same onset to chaos as a network with Gaussian connectivity. Interestingly, the critical properties near transition depend on the shape of the single- neuron input-output transfer function near firing threshold. Finally, we investigate network models with spiking dynamics. When synaptic time constants are slow relative to the mean inverse firing rates, the network undergoes a sharp transition from fast spiking fluctuations and static firing rates to a state with slow chaotic rate fluctuations. When the synaptic time constants are finite, the transition becomes smooth and obeys scaling properties, similar to crossover phenomena in statistical mechanics","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2015-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86927838","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: 142

Dynamics of Fully Coupled Rotators with Unimodal and Bimodal Frequency Distribution 频率分布为单峰和双峰的全耦合旋转体动力学

arXiv: Disordered Systems and Neural Networks Pub Date : 2015-08-04 DOI: 10.1007/978-3-319-28028-8_2

S. Olmi, A. Torcini

引用次数: 6

Approximated Newton Algorithm for the Ising Model Inference Speeds Up Convergence, Performs Optimally and Avoids Over-fitting 近似牛顿算法用于Ising模型推理，加快了收敛速度，实现了最优性能，避免了过拟合

arXiv: Disordered Systems and Neural Networks Pub Date : 2015-07-15 DOI: 10.1103/PhysRevE.94.023301

U. Ferrari

引用次数: 18