Journal of Physics A: Mathematical and Theoretical最新文献

Laplacian operator and its square lattice discretization: Green function vs. Lattice Green function for the flat 2-torus and other related 2D manifolds 拉普拉斯算子及其方格离散化：平面 2-Torus 及其他相关二维流形的格林函数与格网格林函数

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-18 DOI: 10.1088/1751-8121/ad79cc

Malik Mamode

{"title":"Laplacian operator and its square lattice discretization: Green function vs. Lattice Green function for the flat 2-torus and other related 2D manifolds","authors":"Malik Mamode","doi":"10.1088/1751-8121/ad79cc","DOIUrl":"https://doi.org/10.1088/1751-8121/ad79cc","url":null,"abstract":"The paper investigates the truncation error between the Green function and the lattice Green function (LGF) for the Laplacian operator defined on the 2-torus and its discretization on a regular square lattice. Extensions to the cylinder and the rectangular domain with free (or Neumann) boundary conditions are also proposed. In each of these instances, the Green function and its discrete analog are given in exact analytical closed-form allowing to infer accurate estimates as the lattice spacing tends to zero. As expected, it is shown that the continuum limit of the LGF coincides well with the Green function in every case. In particular, the issue of logarithmic singularity regularization of the Green function by the lattice discretization is addressed through two related application examples regarding the rectangular domain, and devoted to the computation of corner-to-corner resistance of an electrical conducting square and the mean first-passage time between the diagonally opposite vertices of a square for a standard Brownian motion, both derived considering the continuum limit.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"38 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The role of mobility in epidemics near criticality 流动性在临界流行病中的作用

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-17 DOI: 10.1088/1751-8121/ad6cb6

Beatrice Nettuno, Davide Toffenetti, Christoph Metzl, Linus Weigand, Florian Raßhofer, Richard Swiderski and Erwin Frey

{"title":"The role of mobility in epidemics near criticality","authors":"Beatrice Nettuno, Davide Toffenetti, Christoph Metzl, Linus Weigand, Florian Raßhofer, Richard Swiderski and Erwin Frey","doi":"10.1088/1751-8121/ad6cb6","DOIUrl":"https://doi.org/10.1088/1751-8121/ad6cb6","url":null,"abstract":"The general epidemic process (GEP), also known as susceptible-infected-recovered model, provides a minimal model of how an epidemic spreads within a population of susceptible individuals who acquire permanent immunization upon recovery. This model exhibits a second-order absorbing state phase transition, commonly studied assuming immobile healthy individuals. We investigate the impact of mobility on the scaling properties of disease spreading near the extinction threshold by introducing two generalizations of GEP, where the mobility of susceptible and recovered individuals is examined independently. In both cases, including mobility violates GEP’s rapidity reversal symmetry and alters the number of absorbing states. The critical dynamics of the models are analyzed through a perturbative renormalization group (RG) approach and large-scale stochastic simulations using a Gillespie algorithm. The RG analysis predicts both models to belong to the same novel universality class describing the critical dynamics of epidemic spreading when the infected individuals interact with a diffusive species and gain immunization upon recovery. At the associated RG fixed point, the immobile species decouples from the dynamics of the infected species, dominated by the coupling with the diffusive species. Numerical simulations in two dimensions affirm our RG results by identifying the same set of critical exponents for both models. Violation of the rapidity reversal symmetry is confirmed by breaking the associated hyperscaling relation. Our study underscores the significance of mobility in shaping population spreading dynamics near the extinction threshold.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"1 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Quantising a Hamiltonian curl force 量化哈密顿卷曲力

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-16 DOI: 10.1088/1751-8121/ad754e

M V Berry and Pragya Shukla

引用次数: 0

Operator dynamics and entanglement in space-time dual Hadamard lattices 时空对偶哈达玛网格中的算子动力学和纠缠

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-16 DOI: 10.1088/1751-8121/ad776a

Pieter W Claeys and Austen Lamacraft

{"title":"Operator dynamics and entanglement in space-time dual Hadamard lattices","authors":"Pieter W Claeys and Austen Lamacraft","doi":"10.1088/1751-8121/ad776a","DOIUrl":"https://doi.org/10.1088/1751-8121/ad776a","url":null,"abstract":"Many-body quantum dynamics defined on a spatial lattice and in discrete time—either as stroboscopic Floquet systems or quantum circuits—has been an active area of research for several years. Being discrete in space and time, a natural question arises: when can such a model be viewed as evolving unitarily in space as well as in time? Models with this property, which sometimes goes by the name space-time duality, have been shown to have a number of interesting features related to entanglement growth and correlations. One natural way in which the property arises in the context of (brickwork) quantum circuits is by choosing dual unitary gates: two site operators that are unitary in both the space and time directions. We introduce a class of models with q states per site, defined on the square lattice by a complex partition function and paremeterized in terms of q × q Hadamard matrices, that have the property of space-time duality. These may interpreted as particular dual unitary circuits or stroboscopically evolving systems, and generalize the well studied self-dual kicked Ising model. We explore the operator dynamics in the case of Clifford circuits, making connections to Clifford cellular automata (Schlingemann et al 2008 J. Math. Phys.49 112104) and in the limit to the classical spatiotemporal cat model of many body chaos (Gutkin et al 2021 Nonlinearity34 2800). We establish integrability and the corresponding conserved charges for a large subfamily and show how the long-range entanglement protocol discussed in the recent paper (Lotkov et al 2022 Phys. Rev. B 105 144306) can be reinterpreted in purely graphical terms and directly applied here.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"65 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248734","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Projected state ensemble of a generic model of many-body quantum chaos 多体量子混沌通用模型的投影态集合

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-16 DOI: 10.1088/1751-8121/ad7211

Amos Chan and Andrea De Luca

{"title":"Projected state ensemble of a generic model of many-body quantum chaos","authors":"Amos Chan and Andrea De Luca","doi":"10.1088/1751-8121/ad7211","DOIUrl":"https://doi.org/10.1088/1751-8121/ad7211","url":null,"abstract":"The projected ensemble is based on the study of the quantum state of a subsystem A conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic quantum system can be defined on the basis of convergence of the projected ensemble to a quantum state design, i.e. a system thermalizes when it becomes indistinguishable, up to the kth moment, from a Haar ensemble of uniformly distributed pure states. Here we consider a random unitary circuit with the brick-wall geometry and analyze its convergence to the Haar ensemble through the frame potential and its mapping to a statistical mechanical problem. This approach allows us to highlight a geometric interpretation of the frame potential based on the existence of a fluctuating membrane, similar to those appearing in the study of entanglement entropies. At large local Hilbert space dimension q, we find that all moments converge simultaneously with a time scaling linearly in the size of region A, a feature previously observed in dual unitary models. However, based on the geometric interpretation, we argue that the scaling at finite q on the basis of rare membrane fluctuations, finding the logarithmic scaling of design times . Our results are supported with numerical simulations performed at q = 2.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"94 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Free fermions, neutrality and modular transformations 自由费米子、中性和模块变换

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-15 DOI: 10.1088/1751-8121/ad77fe

Mbavhalelo Mulokwe and Konstantinos Zoubos

引用次数: 0

Generalized hydrodynamics for the volterra lattice: ballistic and non-ballistic behavior of correlation functions 伏特拉晶格的广义流体力学：相关函数的弹道和非弹道行为

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-15 DOI: 10.1088/1751-8121/ad742b

Guido Mazzuca

{"title":"Generalized hydrodynamics for the volterra lattice: ballistic and non-ballistic behavior of correlation functions","authors":"Guido Mazzuca","doi":"10.1088/1751-8121/ad742b","DOIUrl":"https://doi.org/10.1088/1751-8121/ad742b","url":null,"abstract":"In recent years, a lot of effort has been put in describing the hydrodynamic behavior of integrable systems. In this paper, we describe such picture for the Volterra lattice. Specifically, we are able to explicitly compute the susceptibility matrix and the current-field correlation matrix in terms of the density of states of the Volterra lattice endowed with a Generalized Gibbs ensemble. Furthermore, we apply the theory of linear Generalized Hydrodynamics (GHDs) to describe the Euler scale behavior of the correlation functions. We anticipate that the solution to the GHDs equations develops shocks at ; so this linear approximation does not fully describe the behavior of correlation functions. Intrigued by this fact, we performed several numerical investigations which show that, exactly when the solution to the hydrodynamic equations develops shock, the correlation functions show an highly oscillatory behavior. In view of this empirical observation, we believe that at this point ξ0 the diffusive contribution are not sub-leading corrections to the ballistic transport, but they are of the same order.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"28 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized boson and fermion operators with a maximal total occupation property 具有最大总占据特性的广义玻色子和费米子算子

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-15 DOI: 10.1088/1751-8121/ad77fd

N I Stoilova and J Van der Jeugt

引用次数: 0

Bundled matrix product states represent low-energy excitations faithfully 捆绑矩阵乘积态忠实地代表了低能激发

IF 2.1 3区物理与天体物理

Journal of Physics A: Mathematical and Theoretical Pub Date : 2024-09-12 DOI: 10.1088/1751-8121/ad770f

Thomas E Baker and Negar Seif

引用次数: 0

Quantization, dequantization, and distinguished states 量化、去量化和区分状态