Journal of Statistical Physics最新文献

{"title":"A Central Limit Theorem with Explicit Lyapunov Exponent and Variance for Products of (2times 2) Random Non-invertible Matrices","authors":"Audrey Benson,&nbsp;Hunter Gould,&nbsp;Phanuel Mariano,&nbsp;Grace Newcombe,&nbsp;Joshua Vaidman","doi":"10.1007/s10955-024-03335-3","DOIUrl":"10.1007/s10955-024-03335-3","url":null,"abstract":"<div><p>The theory of products of random matrices and Lyapunov exponents have been widely studied and applied in the fields of biology, dynamical systems, economics, engineering and statistical physics. We consider the product of an i.i.d. sequence of <span>(2times 2)</span> random non-invertible matrices with real entries. Given some mild moment assumptions we prove an explicit formula for the Lyapunov exponent and prove a central limit theorem with an explicit formula for the variance in terms of the entries of the matrices. We also give examples where exact values for the Lyapunov exponent and variance are computed. An important example where non-invertible matrices are essential is the random Hill’s equation, which has numerous physical applications, including the astrophysical orbit problem.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409357","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}

{"title":"Localization in Boundary-Driven Lattice Models","authors":"Michele Giusfredi,&nbsp;Stefano Iubini,&nbsp;Paolo Politi","doi":"10.1007/s10955-024-03324-6","DOIUrl":"10.1007/s10955-024-03324-6","url":null,"abstract":"<div><p>Several systems display an equilibrium condensation transition, where a finite fraction of a conserved quantity is spatially localized. The presence of two conservation laws may induce the emergence of such transition in an out-of-equilibrium setup, where boundaries are attached to different and subcritical heat baths. We study this phenomenon in a class of stochastic lattice models, where the local energy is a general convex function of the local mass, mass and energy being both globally conserved in the isolated system. We obtain exact results for the nonequilibrium steady state (spatial profiles, mass and energy currents, Onsager coefficients) and we highlight important differences between equilibrium and out-of-equilibrium condensation.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03324-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equivariant Divergence Formula for Hyperbolic Chaotic Flows","authors":"Angxiu Ni,&nbsp;Yao Tong","doi":"10.1007/s10955-024-03329-1","DOIUrl":"10.1007/s10955-024-03329-1","url":null,"abstract":"<div><p>We prove the equivariant divergence formula for axiom A flow attractors. It is a pointwisely-defined and recursive formula for perturbation of SRB measures along center-unstable manifolds. It depends on only the zeroth and first order derivatives of the map, the observable, and the perturbation. Hence, the linear response acquires an ‘ergodic theorem’, which means that it can be sampled by recursively computing a few vectors on one orbit.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03329-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimal Control of Underdamped Systems: An Analytic Approach","authors":"Julia Sanders,&nbsp;Marco Baldovin,&nbsp;Paolo Muratore-Ginanneschi","doi":"10.1007/s10955-024-03320-w","DOIUrl":"10.1007/s10955-024-03320-w","url":null,"abstract":"<div><p>Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03320-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Long-Time Anderson Localization for the Nonlinear Random Schrödinger Equation on ({mathbb {Z}}^d)","authors":"Hongzi Cong,&nbsp;Yunfeng Shi,&nbsp;Xiaoqing Wu","doi":"10.1007/s10955-024-03333-5","DOIUrl":"10.1007/s10955-024-03333-5","url":null,"abstract":"<div><p>In this paper, we prove the long-time Anderson localization for the nonlinear random Schrödinger equation on <span>({mathbb {Z}}^d)</span> by using the Birkhoff normal form technique.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248006","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}

{"title":"Emergent Behaviors of the Infinite Set of Lohe Hermitian Sphere Oscillators","authors":"Seung-Yeal Ha,&nbsp;Euntaek Lee","doi":"10.1007/s10955-024-03331-7","DOIUrl":"10.1007/s10955-024-03331-7","url":null,"abstract":"<div><p>We study the emergent behaviors of an infinite number of Lohe Hermitian sphere oscillators on the unit Hermitian sphere. For this, we propose an infinite analogue of the Lohe hermitian sphere model, and present sufficient frameworks leading to collective behaviors in terms of system parameters and initial data. Under some network topology, we show that practical synchronization emerges for a heterogeneous ensemble, whereas exponential synchronization can appear for a homogeneous ensemble. Furthermore we have also derived analogous results for the infinite swarm-sphere model. For the sender network topology in which coupling capacities depend only on the sender index number, we show that there are only two possible asymptotic states, namely complete phase synchrony or bi-cluster configuration for a homogeneous ensemble in a positive coupling regime.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200391","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}

{"title":"A Cascade Model for the Discontinuous Absorbing Phase Transition Between Turbulent and Laminar Flows","authors":"Eric Bertin,&nbsp;Alex Andrix,&nbsp;Gaël Le Godais","doi":"10.1007/s10955-024-03327-3","DOIUrl":"10.1007/s10955-024-03327-3","url":null,"abstract":"<div><p>We introduce a minimal model of energy transfer through scales to describe, at a qualitative level, the subcritical transition between laminar and turbulent flows, viewed in a statistical physics framework as a discontinuous absorbing phase transition. The main control parameter of the model is a Reynolds number that compares energy transfer to viscous dissipation on a large length scale. In spite of its simplicity, the model qualitatively reproduces a number of salient features of the subcritical laminar-turbulent transition, including the existence of an absorbing laminar state, the discontinuous onset of a metastable fluctuating turbulent state above a threshold Reynolds number, and a faster-than-exponential increase of the turbulence lifetime when increasing the Reynolds number. The behavior of the model is also consistent, at high Reynolds number, with the Kolmogorov K41 phenomenology of fully developed turbulence.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200389","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}

{"title":"Absence of Local Conserved Quantity in the Heisenberg Model with Next-Nearest-Neighbor Interaction","authors":"Naoto Shiraishi","doi":"10.1007/s10955-024-03326-4","DOIUrl":"10.1007/s10955-024-03326-4","url":null,"abstract":"<div><p>We rigorously prove that the <span>(S=1/2)</span> anisotropic Heisenberg chain (XYZ chain) with next-nearest-neighbor interaction, which is anticipated to be non-integrable, is indeed non-integrable in the sense that this system has no nontrivial local conserved quantity. Our result covers some important models including the Majumdar–Ghosh model, the Shastry–Sutherland model, and many other zigzag spin chains as special cases. These models are shown to be non-integrable while they have some solvable energy eigenstates. In addition to this result, we provide a pedagogical review of the proof of non-integrability of the <span>(S=1/2)</span> XYZ chain with Z magnetic field, whose proof technique is employed in our result.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03326-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Inverse Cluster Expansion for the Chemical Potential","authors":"Fabio Frommer","doi":"10.1007/s10955-024-03319-3","DOIUrl":"10.1007/s10955-024-03319-3","url":null,"abstract":"<div><p>Interacting particle systems in a finite-volume in equilibrium are often described by a grand-canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly measuring this Hamiltonian is not possible, as such, methods need to be developed to calculate the Hamiltonian potentials from measurable data. In this work, we give an expansion of the chemical potential in terms of the correlation functions of such a system in the thermodynamic limit. This is a justification of a formal approach of Nettleton and Green from the 50’s, that can be seen as an inverse cluster expansion.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03319-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Correction: Subdiffusion in the Presence of Reactive Boundaries: A Generalized Feynman–Kac Approach","authors":"Toby Kay,&nbsp;Luca Giuggioli","doi":"10.1007/s10955-024-03330-8","DOIUrl":"10.1007/s10955-024-03330-8","url":null,"abstract":"","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03330-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}