arXiv: Statistical Mechanics最新文献_第5页

arXiv: Statistical Mechanics Pub Date : 2020-10-26 DOI: 10.1142/9789811223433_0008

csillagászat Fizika

引用次数: 0

Population imbalance for a family of one-dimensional incommensurate models with mobility edges 具有流动边缘的一维不相称模型家庭的人口不平衡

arXiv: Statistical Mechanics Pub Date : 2020-10-19 DOI: 10.1103/PhysRevB.103.184203

Sayantan Roy, S. Mukerjee, M. Kulkarni

{"title":"Population imbalance for a family of one-dimensional incommensurate models with mobility edges","authors":"Sayantan Roy, S. Mukerjee, M. Kulkarni","doi":"10.1103/PhysRevB.103.184203","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.184203","url":null,"abstract":"In this paper, we look at four generalizations of the one dimensional Aubry-Andre-Harper (AAH) model which possess mobility edges. We map out a phase diagram in terms of population imbalance, and look at the system size dependence of the steady state imbalance. We find non-monotonic behaviour of imbalance with system parameters, which contradicts the idea that the relaxation of an initial imbalance is fixed only by the ratio of number of extended states to number of localized states. We propose that there exists dimensionless parameters, which depend on the fraction of single particle localized states, single particle extended states and the mean participation ratio of these states. These ingredients fully control the imbalance in the long time limit and we present numerical evidence of this claim. Among the four models considered, three of them have interesting duality relations and their location of mobility edges are known. One of the models (next nearest neighbour coupling) has no known duality but mobility edge exists and the model has been experimentally realized. Our findings are an important step forward to understanding non-equilibrium phenomena in a family of interesting models with incommensurate potentials.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79524625","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

Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics 自引力玻色气体中的波湍流与非局部非线性光学

arXiv: Statistical Mechanics Pub Date : 2020-10-16 DOI: 10.1103/physreva.102.043318

J. Skipp, V. L’vov, S. Nazarenko

{"title":"Wave turbulence in self-gravitating Bose gases and nonlocal nonlinear optics","authors":"J. Skipp, V. L’vov, S. Nazarenko","doi":"10.1103/physreva.102.043318","DOIUrl":"https://doi.org/10.1103/physreva.102.043318","url":null,"abstract":"We develop the theory of weak wave turbulence in systems described by the Schr\"odinger-Helmholtz equations in two and three dimensions. This model contains as limits both the familiar cubic nonlinear Schr\"odinger equation, and the Schr\"odinger-Newton equations. The latter, in three dimensions, are a nonrelativistic model of fuzzy dark matter which has a nonlocal gravitational self-potential, and in two dimensions they describe nonlocal nonlinear optics in the paraxial approximation. We show that in the weakly nonlinear limit the Schr\"odinger-Helmholtz equations have a simultaneous inverse cascade of particles and a forward cascade of energy. The inverse cascade we interpret as a nonequilibrium condensation process, which is a precursor to structure formation at large scales (for example the formation of galactic dark matter haloes or optical solitons). We show that for the Schr\"odinger-Newton equations in two and three dimensions, and in the two-dimensional nonlinear Schr\"odinger equation, the particle and energy fluxes are carried by small deviations from thermodynamic distributions, rather than the Kolmogorov-Zakharov cascades that are familiar in wave turbulence. We develop a differential approximation model to characterise such \"warm cascade\" states.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84645953","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: 14

Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain 各向异性海森堡量子链磁孤子的半经典量子化

arXiv: Statistical Mechanics Pub Date : 2020-10-14 DOI: 10.21468/SCIPOSTPHYS.10.4.086

Y. Miao, E. Ilievski, O. Gamayun

引用次数: 1

Unsupervised learning of topological phase transitions using the Calinski-Harabaz index 使用Calinski-Harabaz指数的拓扑相变的无监督学习

arXiv: Statistical Mechanics Pub Date : 2020-10-13 DOI: 10.1103/PHYSREVRESEARCH.3.013074

Jie-Ming Wang, Wanzhou Zhang, Tian Hua, T. Wei

{"title":"Unsupervised learning of topological phase transitions using the Calinski-Harabaz index","authors":"Jie-Ming Wang, Wanzhou Zhang, Tian Hua, T. Wei","doi":"10.1103/PHYSREVRESEARCH.3.013074","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.3.013074","url":null,"abstract":"Machine learning methods have been recently applied to learning phases of matter and transitions between them. Of particular interest is the topological phase transition, such as in the XY model, which can be difficult for unsupervised learning such as the principal component analysis. Recently, authors of [Nature Physics textbf{15},790 (2019)] employed the diffusion-map method for identifying topological order and were able to determine the BKT phase transition of the XY model, specifically via the intersection of the average cluster distance $bar{D}$ and the within cluster dispersion $barsigma$ (when the different clusters vary from separation to mixing together). However, sometimes it is not easy to find the intersection if $bar{D}$ or $bar{sigma}$ does not change too much due to topological constraint. In this paper, we propose to use the Calinski-Harabaz ($ch$) index, defined roughly as the ratio $bar D/bar sigma$, to determine the critical points, at which the $ch$ index reaches a maximum or minimum value, or jump sharply. We examine the $ch$ index in several statistical models, including ones that contain a BKT phase transition. For the Ising model, the peaks of the quantity $ch$ or its components are consistent with the position of the specific heat maximum. For the XY model both on the square lattices and honeycomb lattices, our results of the $ch$ index show the convergence of the peaks over a range of the parameters $varepsilon/varepsilon_0$ in the Gaussian kernel. We also examine the generalized XY model with $q=2$ and $q=8$ and at the value away from the pure XY limit. Our method is thus useful to both topological and non-topological phase transitions and can achieve accuracy as good as supervised learning methods previously used in these models, and may be used for searching phases from experimental data.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72650807","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: 23

Interfacial-curvature-driven coarsening in mass-conserved reaction-diffusion systems 质量守恒反应扩散系统中界面曲率驱动的粗化

arXiv: Statistical Mechanics Pub Date : 2020-10-08 DOI: 10.1103/PhysRevResearch.3.023198

Michio Tateno, S. Ishihara

{"title":"Interfacial-curvature-driven coarsening in mass-conserved reaction-diffusion systems","authors":"Michio Tateno, S. Ishihara","doi":"10.1103/PhysRevResearch.3.023198","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.3.023198","url":null,"abstract":"Mass conservation in chemical species appears in a broad class of reaction-diffusion systems (RDs) and is known to bring about coarsening of the pattern in chemical concentration. Recent theoretical studies on RDs with mass conservation (MCRDs) reported that the interfacial curvature between two states contributes to the coarsening process, reminiscent of phase separation phenomena. However, since MCRDs do not presuppose a variational principle, it is largely unknown whether description of surface tension is operative or not. In this study, we numerically and theoretically explore the coarsening process of patterns in MCRDs in two and three dimensions. We identify the parameter regions where the homogeneous steady state becomes stable, unstable, and metastable. In the unstable region, pattern formation is triggered by usual Turing instability, whereas in the metastable region, nucleation-growth-type pattern formation is observed. In the later stage, spherical droplet patterns are observed in both regions, where they obey a relation similar to the Young-Laplace law and coarsen following the evaporation-condensation mechanism. These results demonstrate that in the presence of a conserved variable, a physical quantity similar to surface tension is relevant to MCRDs, which provides new insight into molecular self-assembly driven by chemical reactions.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82115300","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: 1

Topology Protects Robust Global Cycles in Stochastic Systems 拓扑保护随机系统的鲁棒全局循环

arXiv: Statistical Mechanics Pub Date : 2020-10-06 DOI: 10.1016/J.BPJ.2020.11.1419

Evelyn Tang, J. Agudo-Canalejo, R. Golestanian

引用次数: 1

arXiv: Statistical Mechanics Pub Date : 2020-10-06 DOI: 10.1016/J.CHAOS.2021.110790

T. Mitra, Tomal Hossain, S. Banerjee, Md. Kamrul Hassan

引用次数: 4

Integrable quantum spin chains with free fermionic and parafermionic spectrum 具有自由费米子和准费米子谱的可积量子自旋链

arXiv: Statistical Mechanics Pub Date : 2020-10-02 DOI: 10.1103/physrevb.102.235170

F. C. Alcaraz, R. A. Pimenta

{"title":"Integrable quantum spin chains with free fermionic and parafermionic spectrum","authors":"F. C. Alcaraz, R. A. Pimenta","doi":"10.1103/physrevb.102.235170","DOIUrl":"https://doi.org/10.1103/physrevb.102.235170","url":null,"abstract":"We present a general study of the large family of exact integrable quantum chains with multispin interactions introduced recently in cite{AP2020}. The exact integrability follows from the algebraic properties of the energy density operators defining the quantum chains. The Hamiltonians are characterized by a parameter $p=1,2,dots$ related to the number of interacting spins in the multispin interaction. In the general case the quantum spins are of infinite dimension. In special cases, characterized by the parameter $N=2,3,ldots$, the quantum chains describe the dynamics of $Z(N)$ quantum spin chains. The simplest case $p=1$ corresponds to the free fermionic quantum Ising chain ($N=2$) or the $Z(N)$ free parafermionic quantum chain. The eigenenergies of the quantum chains are given in terms of the roots of special polynomials, and for general values of $p$ the quantum chains are characterized by a free fermionic ($N=2$) or free parafermionic ($N>2$) eigenspectrum. The models have a special critical point when all coupling constants are equal. At this point the ground-state energy is exactly calculated in the bulk limit, and our analytical and numerical analyses indicate that the models belong to universality classes of critical behavior with dynamical critical exponent $z = (p+1)/N$ and specific-heat exponent $alpha = max{0,1-(p+1)/N}$.","PeriodicalId":8473,"journal":{"name":"arXiv: Statistical Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84537155","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: 12

Transition between chaotic and stochastic universality classes of kinetic roughening 动力学粗化的混沌和随机普适性之间的转换

arXiv: Statistical Mechanics Pub Date : 2020-09-24 DOI: 10.1103/PHYSREVRESEARCH.3.L012020

Enrique Rodríguez-Fernández, R. Cuerno

引用次数: 3