arXiv: Statistical Mechanics最新文献_第8页

Finite temperature off-diagonal long-range order for interacting bosons 相互作用玻色子的有限温度非对角长程序

arXiv: Statistical Mechanics Pub Date : 2020-07-02 DOI: 10.1103/physrevb.102.184510

A. Colcelli, N. Defenu, G. Mussardo, A. Trombettoni

{"title":"Finite temperature off-diagonal long-range order for interacting bosons","authors":"A. Colcelli, N. Defenu, G. Mussardo, A. Trombettoni","doi":"10.1103/physrevb.102.184510","DOIUrl":"https://doi.org/10.1103/physrevb.102.184510","url":null,"abstract":"Characterizing the scaling with the total particle number ($N$) of the largest eigenvalue of the one--body density matrix ($lambda_0$), provides informations on the occurrence of the off-diagonal long-range order (ODLRO) according to the Penrose-Onsager criterion. Setting $lambda_0sim N^{mathcal{C}_0}$, then $mathcal{C}_0=1$ corresponds to ODLRO. The intermediate case, $0<mathcal{C}_0<1$, corresponds for translational invariant systems to the power-law decaying of (non-connected) correlation functions and it can be seen as identifying quasi-long-range order. The goal of the present paper is to characterize the ODLRO properties encoded in $mathcal{C}_0$ [and in the corresponding quantities $mathcal{C}_{k neq 0}$ for excited natural orbitals] exhibited by homogeneous interacting bosonic systems at finite temperature for different dimensions. We show that $mathcal{C}_{k neq 0}=0$ in the thermodynamic limit. In $1D$ it is $mathcal{C}_0=0$ for non-vanishing temperature, while in $3D$ $mathcal{C}_0=1$ ($mathcal{C}_0=0$) for temperatures smaller (larger) than the Bose-Einstein critical temperature. We then focus our attention to $D=2$, studying the $XY$ and the Villain models, and the weakly interacting Bose gas. The universal value of $mathcal{C}_0$ near the Berezinskii--Kosterlitz--Thouless temperature $T_{BKT}$ is $7/8$. The dependence of $mathcal{C}_0$ on temperatures between $T=0$ (at which $mathcal{C}_0=1$) and $T_{BKT}$ is studied in the different models. An estimate for the (non-perturbative) parameter $xi$ entering the equation of state of the $2D$ Bose gases, is obtained using low temperature expansions and compared with the Monte Carlo result. We finally discuss a double jump behaviour for $mathcal{C}_0$, and correspondingly of the anomalous dimension $eta$, right below $T_{BKT}$ in the limit of vanishing interactions.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80762133","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: 5

Renormalization group approach to spontaneous stochasticity 自发随机性的重整化群方法

arXiv: Statistical Mechanics Pub Date : 2020-07-02 DOI: 10.1103/PHYSREVRESEARCH.2.043161

G. Eyink, Dmytro Bandak

{"title":"Renormalization group approach to spontaneous stochasticity","authors":"G. Eyink, Dmytro Bandak","doi":"10.1103/PHYSREVRESEARCH.2.043161","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.043161","url":null,"abstract":"We develop a theoretical approach to ``spontaneous stochasticity'' in classical dynamical systems that are nearly singular and weakly perturbed by noise. This phenomenon is associated to a breakdown in uniqueness of solutions for fixed initial data and underlies many fundamental effects of turbulence (unpredictability, anomalous dissipation, enhanced mixing). Based upon analogy with statistical-mechanical critical points at zero temperature, we elaborate a renormalization group (RG) theory that determines the universal statistics obtained for sufficiently long times after the precise initial data are ``forgotten''. We apply our RG method to solve exactly the ``minimal model'' of spontaneous stochasticity given by a 1D singular ODE. Generalizing prior results for the infinite-Reynolds limit of our model, we obtain the RG fixed points that characterize the spontaneous statistics in the near-singular, weak-noise limit, determine the exact domain of attraction of each fixed point, and derive the universal approach to the fixed points as a singular large-deviations scaling, distinct from that obtained by the standard saddle-point approximation to stochastic path-integrals in the zero-noise limit. We present also numerical simulation results that verify our analytical predictions, propose possible experimental realizations of the ``minimal model'', and discuss more generally current empirical evidence for ubiquitous spontaneous stochasticity in Nature. Our RG method can be applied to more complex, realistic systems and some future applications are briefly outlined.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83977125","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: 6

Disorder-free localization and many-body quantum scars from magnetic frustration 无无序定位和多体量子磁损伤

arXiv: Statistical Mechanics Pub Date : 2020-07-02 DOI: 10.1103/physrevb.102.224303

P. McClarty, M. Haque, Arnab Sen, J. Richter

{"title":"Disorder-free localization and many-body quantum scars from magnetic frustration","authors":"P. McClarty, M. Haque, Arnab Sen, J. Richter","doi":"10.1103/physrevb.102.224303","DOIUrl":"https://doi.org/10.1103/physrevb.102.224303","url":null,"abstract":"Geometrical frustration has led to rich insights into condensed matter physics, especially as a mechansim to produce exotic low energy states of matter. Here we show that frustration provides a natural vehicle to generate models exhibiting anomalous thermalization of various types within high energy states. We consider three classes of non-integrable translationally invariant frustrated spin models: (I) systems with local conserved quantities where the number of symmetry sectors grows exponentially with the system size but more slowly than the Hilbert space dimension (II) systems with exact eigenstates that are singlet coverings and (III) flat band systems hosting magnon crystals. We argue that several 1D and 2D models from class (I) exhibit disorder-free localization in high energy states so that information propagation is dynamically inhibited on length scales greater than a few lattice spacings. We further show that models of class (II) and (III) exhibit quantum many-body scars $-$ eigenstates of non-integrable Hamiltonians with finite energy density and anomalously low entanglement entropy. Our results demonstrate that magnetic frustration supplies a means to systematically construct classes of non-integrable models exhibiting anomalous thermalization in mid-spectrum states.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81812825","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

Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems 具有多个储层的粗粒度熵生产:揭示时间尺度和生物启发系统中的详细平衡的作用

arXiv: Statistical Mechanics Pub Date : 2020-07-01 DOI: 10.1103/PHYSREVRESEARCH.2.043257

D. M. Busiello, D. Gupta, A. Maritan

{"title":"Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems","authors":"D. M. Busiello, D. Gupta, A. Maritan","doi":"10.1103/PHYSREVRESEARCH.2.043257","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.043257","url":null,"abstract":"A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles exchanging heat with different baths, constitute some interesting examples of such a modelization. Moreover, they usually operate out of equilibrium, being characterized by a net production of entropy, which entails a constrained efficiency. Hitherto, in order to investigate multiple processes simultaneously driving a system, all theoretical approaches deal with them independently, at a coarse-grained level, or employing a separation of time-scales. Here, we explicitly take in consideration the interplay among time-scales of different processes, and whether or not their own evolution eventually relaxes toward an equilibrium state in a given sub-space. We propose a general framework for multiple coupling, from which the well-known formulas for the entropy production can be derived, depending on the available information about each single process. Furthermore, when one of the processes does not equilibrate in its sub-space, even if much faster than all the others, it introduces a finite correction to the entropy production. We employ our framework in various simple and pedagogical examples, for which such a corrective term can be related to a typical scaling of physical quantities in play.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86379253","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: 10

Experimental Measurement of Relative Path Probabilities and Stochastic Actions 相对路径概率和随机行为的实验测量

arXiv: Statistical Mechanics Pub Date : 2020-06-30 DOI: 10.1103/PhysRevX.11.031022

Jannes Gladrow, U. Keyser, R. Adhikari, Julian Kappler

引用次数: 3

Entanglement entropy of fermions from Wigner functions: Excited states and open quantum systems 维格纳函数中费米子的纠缠熵:激发态和开放量子系统

arXiv: Statistical Mechanics Pub Date : 2020-06-29 DOI: 10.1103/physrevb.102.184306

Saranyo Moitra, R. Sensarma

{"title":"Entanglement entropy of fermions from Wigner functions: Excited states and open quantum systems","authors":"Saranyo Moitra, R. Sensarma","doi":"10.1103/physrevb.102.184306","DOIUrl":"https://doi.org/10.1103/physrevb.102.184306","url":null,"abstract":"We formulate a new ``Wigner characteristics'' based method to calculate entanglement entropies of subsystems of Fermions using Keldysh field theory. This bypasses the requirements of working with complicated manifolds for calculating Renyi entropies for many body systems. We provide an exact analytic formula for Renyi and von-Neumann entanglement entropies of non-interacting open quantum systems, which are initialised in arbitrary Fock states. We use this formalism to look at entanglement entropies of momentum Fock states of one-dimensional Fermions. We show that the entanglement entropy of a Fock state can scale either logarithmically or linearly with subsystem size, depending on whether the number of discontinuities in the momentum distribution is smaller or larger than the subsystem size. This classification of states in terms number of blocks of occupied momenta allows us to analytically estimate the number of critical and non-critical Fock states for a particular subsystem size. We also use this formalism to describe entanglement dynamics of an open quantum system starting with a single domain wall at the center of the system. Using entanglement entropy and mutual information, we understand the dynamics in terms of coherent motion of the domain wall wavefronts, creation and annihilation of domain walls and incoherent exchange of particles with the bath.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76943352","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: 7

Classical and quantum stochastic thermodynamics 经典和量子随机热力学

arXiv: Statistical Mechanics Pub Date : 2020-06-25 DOI: 10.1590/1806-9126-rbef-2020-0210

M. J. Oliveira

引用次数: 4

Origin of universality in the onset of superdiffusion in Lévy walks 在lsamvy游动中超扩散开始时的普遍性起源

arXiv: Statistical Mechanics Pub Date : 2020-06-21 DOI: 10.1103/physrevresearch.2.032042

Asaf Miron

引用次数: 1

Speck of chaos 混沌的斑点

arXiv: Statistical Mechanics Pub Date : 2020-06-18 DOI: 10.1103/physrevresearch.2.043034

L. F. Santos, F. P'erez-Bernal, E. J. Torres-Herrera

引用次数: 31

Fermion-induced dynamical critical point 费米子诱导的动力学临界点

arXiv: Statistical Mechanics Pub Date : 2020-06-16 DOI: 10.1103/PHYSREVB.103.125116

Shuai Yin, Shao-Kai Jian

{"title":"Fermion-induced dynamical critical point","authors":"Shuai Yin, Shao-Kai Jian","doi":"10.1103/PHYSREVB.103.125116","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.125116","url":null,"abstract":"Dynamical phase transition (DPT) characterizes the abrupt change of dynamical properties in nonequilibrium quantum many-body systems. It has been demonstrated that extra quantum fluctuating modes besides the conventional order parameter field can drastically change the properties of equilibrium phase transitions. However, the counterpart phenomena in DPTs have rarely been explored. Here, we study the DPT in the Dirac system after a sudden quench, and find that the fermion fluctuations can round a putative first-order DPT into a dynamical critical point, which is referred to as a fermion-induced dynamical critical point (FIDCP). It is also a nonthermal critical point, in which the universal short-time scaling behavior emerges despite the system goes through a first-order transition after thermalization. In the novel scenario of FIDCP, the quantum Yukawa coupling $g_q$ is indispensable for inducing the FIDCP albeit irrelevant in the infrared scale. We call these variables {it indispensable irrelevant scaling variables}. Moreover, a dynamical tricritical point which separates the first-order DPT and the FIDCP is discovered by tuning this indispensable irrelevant scaling variable. We further mention possible experimental realizations.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":"22 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81873394","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