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Dynamics of the Infinite Discrete Nonlinear Schrödinger Equation 无限离散非线性薛定谔方程的动力学原理
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-26 DOI: 10.1007/s10955-024-03374-w
Aleksis Vuoksenmaa
{"title":"Dynamics of the Infinite Discrete Nonlinear Schrödinger Equation","authors":"Aleksis Vuoksenmaa","doi":"10.1007/s10955-024-03374-w","DOIUrl":"10.1007/s10955-024-03374-w","url":null,"abstract":"<div><p>The discrete nonlinear Schrödinger equation on <span>({mathbb Z}^d)</span>, <span>(d ge 1)</span> is an example of a dispersive nonlinear wave system. Being a Hamiltonian system that conserves also the <span>(ell ^2({mathbb Z}^d))</span>-norm, the well-posedness of the corresponding Cauchy problem follows for square-summable initial data. In this paper, we prove that the well-posedness continues to hold for initial data that can grow towards infinity, namely anything that has at most a certain power law growth far away from the origin. The growth condition is loose enough to guarantee that, at least in dimension <span>(d=1)</span>, initial data sampled from any reasonable equilibrium distribution of the defocusing DNLS satisfies it almost surely.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03374-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714191","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}
引用次数: 0
Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov–Poisson 量子优化传输伪计量学中的增强稳定性：从哈特里到弗拉索夫-泊松
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03367-9
Mikaela Iacobelli, Laurent Lafleche
{"title":"Enhanced Stability in Quantum Optimal Transport Pseudometrics: From Hartree to Vlasov–Poisson","authors":"Mikaela Iacobelli,&nbsp;Laurent Lafleche","doi":"10.1007/s10955-024-03367-9","DOIUrl":"10.1007/s10955-024-03367-9","url":null,"abstract":"<div><p>In this paper we establish almost-optimal stability estimates in quantum optimal transport pseudometrics for the semiclassical limit of the Hartree dynamics to the Vlasov–Poisson equation, in the regime where the solutions have bounded densities. We combine Golse and Paul’s method from [Arch Ration Mech Anal 223:57–94, 2017], which uses a semiclassical version of the optimal transport distance and which was adapted to the case of the Coulomb and gravitational interactions by the second author in [J Stat Phys 177:20–60, 2019], with a new approach developed by the first author in [Arch Ration Mech Anal 244:27–50, 2022] to quantitatively improve stability estimates in kinetic theory.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03367-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694769","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}
引用次数: 0
Relativistic One-Dimensional Billiards 相对论一维台球
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03364-y
Alfonso Artigue
{"title":"Relativistic One-Dimensional Billiards","authors":"Alfonso Artigue","doi":"10.1007/s10955-024-03364-y","DOIUrl":"10.1007/s10955-024-03364-y","url":null,"abstract":"<div><p>In this article we study the dynamics of one-dimensional relativistic billiards containing particles with positive and negative energy. We study configurations with two identical positive masses and symmetric positions with two massless particles between them of negative energy and symmetric positions. We show that such systems have finitely many collisions in any finite time interval. This is due to a phenomenon we call <i>tachyonic collision</i>, which occur at small scales and produce changes in the sign of the energy of individual particles. We also show that depending on the initial parameters the solutions can be bounded with certain periodicity or unbounded while obeying an inverse square law at large distances.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694832","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 Pirogov–Sinai Theory for Infinite Interactions 无限相互作用的皮罗戈夫-西奈理论
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03370-0
A. Mazel, I. Stuhl, Y. Suhov
{"title":"The Pirogov–Sinai Theory for Infinite Interactions","authors":"A. Mazel,&nbsp;I. Stuhl,&nbsp;Y. Suhov","doi":"10.1007/s10955-024-03370-0","DOIUrl":"10.1007/s10955-024-03370-0","url":null,"abstract":"<div><p>The purpose of this note is to consider a number of straightforward generalizations of the Pirogov–Sinai theory which can be covered by minor additions to the canonical texts. These generalizations are well-known among the adepts of the Pirogov–Sinai theory but are lacking formal references.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142714389","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
Geometric Aspects of a Spin Chain 自旋链的几何方面
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03332-6
Michael Entov, Leonid Polterovich, Lenya Ryzhik
{"title":"Geometric Aspects of a Spin Chain","authors":"Michael Entov,&nbsp;Leonid Polterovich,&nbsp;Lenya Ryzhik","doi":"10.1007/s10955-024-03332-6","DOIUrl":"10.1007/s10955-024-03332-6","url":null,"abstract":"<div><p>We discuss non-equilibrium thermodynamics of the mean-field Ising model from a geometric perspective, focusing on the thermodynamic limit. When the number of spins is finite, the Gibbs equilibria form a smooth Legendrian submanifold in the thermodynamic phase space whose points describe the stable macroscopic states of the system. We describe the convergence of these smooth Legendrian submanifolds, as the number of spins goes to infinity, to a singular Legendrian submanifold, admitting an analytic continuation that contains both the stable and metastable states. We also discuss the relaxation to a Gibbs equilibrium when the physical parameters are changed abruptly. The relaxation is defined via the gradient flow of the free energy with respect to the Wasserstein metric on microscopic states, that is, in the geometric language, via the gradient flow of the generating function of the equilibrium Legendrian with respect to the ghost variables. This leads to a discrete Fokker-Planck equation when the number of spins is finite. We show that in the thermodynamic limit this description is closely related to the seminal model of relaxation proposed by Glauber. Finally, we find a special range of parameters where such relaxation happens instantaneously, along the Reeb chords connecting the initial and the terminal Legendrian submanifolds.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694831","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
Propagation of Chaos and Phase Transition in a Stochastic Model for a Social Network 社交网络随机模型中的混沌传播与相变
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-25 DOI: 10.1007/s10955-024-03365-x
Eva Löcherbach, Kádmo Laxa
{"title":"Propagation of Chaos and Phase Transition in a Stochastic Model for a Social Network","authors":"Eva Löcherbach,&nbsp;Kádmo Laxa","doi":"10.1007/s10955-024-03365-x","DOIUrl":"10.1007/s10955-024-03365-x","url":null,"abstract":"<div><p>We consider a model for a social network with N interacting social actors. This model is a system of interacting marked point processes in which each point process indicates the successive times in which a social actor expresses a “favorable” (<span>(+1)</span>) or “contrary” (<span>(-1)</span>) opinion. The orientation and the rate at which an actor expresses an opinion is influenced by the social pressure exerted on this actor. The social pressure of an actor is reset to 0 when the actor expresses an opinion, and simultaneously the social pressures on all the other actors change by h/N in the direction of the opinion that was just expressed. We prove propagation of chaos of the system, as N diverges to infinity, to a limit nonlinear jumping stochastic differential equation. Moreover, we prove that under certain conditions the limit system exhibits a phase transition described as follows. If h is smaller or equal than a certain threshold, the limit system has only the null Dirac measure as an invariant probability measure, corresponding to a vanishing social pressure on all actors. However, if h is greater than the threshold, the system has two additional non-trivial invariant probability measures. One of these measures has support on the positive real numbers and the other is obtained by symmetrization with respect to 0, having thus support on the negative real numbers.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142694799","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
Mean Field Limits of a Class of Conservative Systems with Position-Dependent Transition Rates 一类保守系统的平均场极限与位置相关的转换率
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-22 DOI: 10.1007/s10955-024-03372-y
Xiaofeng Xue
{"title":"Mean Field Limits of a Class of Conservative Systems with Position-Dependent Transition Rates","authors":"Xiaofeng Xue","doi":"10.1007/s10955-024-03372-y","DOIUrl":"10.1007/s10955-024-03372-y","url":null,"abstract":"<div><p>In this paper, we are concerned with a class of conservative systems including asymmetric exclusion processes and zero-range processes as examples, where some particles are initially placed on <i>N</i> positions. A particle jumps from a position to another at a rate depending on the coordinates of these two positions and the number of particles on these two positions. We show that the hydrodynamic limit of our model is driven by a nonlinear function-valued ordinary differential equation which is consistent with a mean field analysis. Furthermore, in the case where the number of particles on all positions are bounded by <span>(mathcal {K}&lt;+infty )</span>, we show that the fluctuation of our model is driven by a generalized Ornstein–Uhlenbeck process. A crucial step in the proofs of our main results is to show that the number of particles on different positions are approximately independent by utilizing a graphical method.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142691927","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
Dynamical Transition of Quantum Scrambling in a Non-Hermitian Floquet Synthetic System 非ermitian Floquet 合成系统中的量子争用动态转变
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-21 DOI: 10.1007/s10955-024-03368-8
Liang Huo, Han Ke, Wen-Lei Zhao
{"title":"Dynamical Transition of Quantum Scrambling in a Non-Hermitian Floquet Synthetic System","authors":"Liang Huo,&nbsp;Han Ke,&nbsp;Wen-Lei Zhao","doi":"10.1007/s10955-024-03368-8","DOIUrl":"10.1007/s10955-024-03368-8","url":null,"abstract":"<div><p>We investigate the dynamics of quantum scrambling, characterized by the out-of-time ordered correlators (OTOCs), in a non-Hermitian quantum kicked rotor subjected to quasi-periodical modulation in kicking potential. Quasi-periodic modulation with incommensurate frequencies creates a high-dimensional synthetic space, where two different phases of quantum scrambling emerge: the freezing phase characterized by the rapid increase of OTOCs towards saturation, and the chaotic scrambling phase featured by the linear growth of OTOCs with time. We find the dynamical transition from the freezing phase to the chaotic scrambling phase, which is assisted by increasing the real part of the kicking potential along with a zero value of its imaginary part. The opposite transition occurs with the increase in the imaginary part of the kicking potential, demonstrating the suppression of quantum scrambling by non-Hermiticity. The underlying mechanism is uncovered by the extension of the Floquet theory. Possible applications in the field of quantum information are discussed.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679776","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
Maxentropy Completion and Properties of Some Partially Defined Stationary Markov Chains 某些部分定义的固定马尔可夫链的最大熵完备性及其特性
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-21 DOI: 10.1007/s10955-024-03369-7
Pierre Collet, Servet Martínez
{"title":"Maxentropy Completion and Properties of Some Partially Defined Stationary Markov Chains","authors":"Pierre Collet,&nbsp;Servet Martínez","doi":"10.1007/s10955-024-03369-7","DOIUrl":"10.1007/s10955-024-03369-7","url":null,"abstract":"<div><p>We consider a stationary Markovian evolution with values on a finite disjointly partitioned set space <span>(Isqcup mathcal{E})</span>. The evolution is visible (in the sense of knowing the transition probabilities) on the states in <i>I</i> but not for the states in <span>(mathcal{E})</span>. One only knows some partial information on the transition probabilities on <span>(mathcal{E})</span>, the input and output transition probabilities and some constraints of the transition probabilities on <span>(mathcal{E})</span>. Under some conditions we supply the transition probabilities on <span>(mathcal{E})</span> that satisfies the maximum entropy principle.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 12","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142679775","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
Hidden Temperature in the KMP Model KMP 模型中隐藏的温度
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-11-12 DOI: 10.1007/s10955-024-03363-z
Anna de Masi, Pablo A. Ferrari, Davide Gabrielli
{"title":"Hidden Temperature in the KMP Model","authors":"Anna de Masi,&nbsp;Pablo A. Ferrari,&nbsp;Davide Gabrielli","doi":"10.1007/s10955-024-03363-z","DOIUrl":"10.1007/s10955-024-03363-z","url":null,"abstract":"<div><p>In the Kipnis Marchioro Presutti model a positive energy <span>(zeta _i)</span> is associated with each vertex <i>i</i> of a finite graph with a boundary. When a Poisson clock rings at an edge <i>ij</i> with energies <span>(zeta _i,zeta _j)</span>, those values are substituted by <span>(U(zeta _i+zeta _j))</span> and <span>((1-U)(zeta _i+zeta _j))</span>, respectively, where <i>U</i> is a uniform random variable in (0, 1). A value <span>(T_jge 0)</span> is fixed at each boundary vertex <i>j</i>. The dynamics is defined in such way that the resulting Markov process <span>(zeta (t))</span>, satisfies that <span>(zeta _j(t))</span> is exponential with mean <span>(T_j)</span>, for each boundary vertex <i>j</i>, for all <i>t</i>. We show that the invariant measure is the distribution of a vector <span>(zeta )</span> with coordinates <span>(zeta _i=T_iX_i)</span>, where <span>(X_i)</span> are iid exponential(1) random variables, the law of <i>T</i> is the invariant measure for an opinion random averaging/gossip model with the same boundary conditions of <span>(zeta )</span>, and the vectors <i>X</i> and <i>T</i> are independent. The result confirms a conjecture based on the large deviations of the model. When the graph is one-dimensional, we bound the correlations of the invariant measure and perform the hydrostatic limit. We show that the empirical measure of a configuration chosen with the invariant measure converges to the linear interpolation of the boundary values.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 11","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142600628","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
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