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Analysis of the Dynamics in Linear Chain Models by means of Generalized Langevin Equations 利用广义朗文方程分析线性链模型的动态性
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-05-04 DOI: 10.1007/s10955-024-03274-z
Fabian Koch, Suvendu Mandal, Tanja Schilling
{"title":"Analysis of the Dynamics in Linear Chain Models by means of Generalized Langevin Equations","authors":"Fabian Koch,&nbsp;Suvendu Mandal,&nbsp;Tanja Schilling","doi":"10.1007/s10955-024-03274-z","DOIUrl":"10.1007/s10955-024-03274-z","url":null,"abstract":"<div><p>We analyse the motion of one particle in a polymer chain. For this purpose, we use the framework of the exact (non-stationary) generalized Langevin equation that can be derived from first principles via the projection-operator method. Our focus lies on determining memory kernels from either exact expressions for autocorrelation functions or from simulation data. We increase the complexity of the underlying system starting out from one-dimensional harmonic chains and ending with a polymer driven through a polymer melt. Here, the displacement or the velocity of an individual particle in the chain serves as the observable. The central result is that the time-window in which the memory kernels show structure before they rapidly decay decreases with increasing complexity of the system.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03274-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889772","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
Random-Matrix Models of Monitored Quantum Circuits 监控量子电路的随机矩阵模型
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-05-03 DOI: 10.1007/s10955-024-03273-0
Vir B. Bulchandani, S. L. Sondhi, J. T. Chalker
{"title":"Random-Matrix Models of Monitored Quantum Circuits","authors":"Vir B. Bulchandani,&nbsp;S. L. Sondhi,&nbsp;J. T. Chalker","doi":"10.1007/s10955-024-03273-0","DOIUrl":"10.1007/s10955-024-03273-0","url":null,"abstract":"<div><p>We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter–Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker–Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov–Mello–Pereyra–Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03273-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140888696","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
Exponential Stability and Hypoelliptic Regularization for the Kinetic Fokker–Planck Equation with Confining Potential 具有约束势的动力学福克-普朗克方程的指数稳定性和次椭圆正则化
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-27 DOI: 10.1007/s10955-024-03263-2
Anton Arnold, Gayrat Toshpulatov
{"title":"Exponential Stability and Hypoelliptic Regularization for the Kinetic Fokker–Planck Equation with Confining Potential","authors":"Anton Arnold,&nbsp;Gayrat Toshpulatov","doi":"10.1007/s10955-024-03263-2","DOIUrl":"10.1007/s10955-024-03263-2","url":null,"abstract":"<div><p>This paper is concerned with a modified entropy method to establish the large-time convergence towards the (unique) steady state, for kinetic Fokker–Planck equations with non-quadratic confinement potentials in whole space. We extend previous approaches by analyzing Lyapunov functionals with non-constant weight matrices in the dissipation functional (a generalized Fisher information). We establish exponential convergence in a weighted <span>(H^1)</span>-norm with rates that become sharp in the case of quadratic potentials. In the defective case for quadratic potentials, i.e. when the drift matrix has non-trivial Jordan blocks, the weighted <span>(L^2)</span>-distance between a Fokker–Planck-solution and the steady state has always a sharp decay estimate of the order <span>(mathcal Obig ( (1+t)e^{-tnu /2}big ))</span>, with <span>(nu )</span> the friction parameter. The presented method also gives new hypoelliptic regularization results for kinetic Fokker–Planck equations (from a weighted <span>(L^2)</span>-space to a weighted <span>(H^1)</span>-space).</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03263-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811469","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
Extending Cercignani’s Conjecture Results from Boltzmann to Boltzmann–Fermi–Dirac Equation 将塞西尼亚尼猜想的结果从玻尔兹曼扩展到玻尔兹曼-费米-狄拉克方程
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-27 DOI: 10.1007/s10955-024-03262-3
Thomas Borsoni
{"title":"Extending Cercignani’s Conjecture Results from Boltzmann to Boltzmann–Fermi–Dirac Equation","authors":"Thomas Borsoni","doi":"10.1007/s10955-024-03262-3","DOIUrl":"10.1007/s10955-024-03262-3","url":null,"abstract":"<div><p>We establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy–entropy production inequality from one case to the other; therefore providing entropy–entropy production inequalities for the Boltzmann–Fermi–Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csiszár–Kullback–Pinsker inequality to weighted <span>(L^p)</span> norms, <span>(1 le p le 2)</span> and a wide class of entropies.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811438","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 Physisorbate-Layer Problem Arising in Kinetic Theory of Gas–Surface Interaction 气-面相互作用动力学理论中出现的物理贝特层问题
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-27 DOI: 10.1007/s10955-024-03270-3
Kazuo Aoki, Vincent Giovangigli, François Golse, Shingo Kosuge
{"title":"The Physisorbate-Layer Problem Arising in Kinetic Theory of Gas–Surface Interaction","authors":"Kazuo Aoki,&nbsp;Vincent Giovangigli,&nbsp;François Golse,&nbsp;Shingo Kosuge","doi":"10.1007/s10955-024-03270-3","DOIUrl":"10.1007/s10955-024-03270-3","url":null,"abstract":"<div><p>A half-space problem of a linear kinetic equation for gas molecules physisorbed close to a solid surface, relevant to a kinetic model of gas–surface interaction and derived by Aoki et al. (Phys. Rev. E 106:035306, 2022), is considered. The equation contains a confinement potential in the vicinity of the solid surface and an interaction term between gas molecules and phonons. It is proved that a unique solution exists when the incoming molecular flux is specified at infinity. This validates the natural observation that the half-space problem serves as the boundary condition for the Boltzmann equation. It is also proved that the sequence of approximate solutions used for the existence proof converges exponentially fast. In addition, numerical results showing the details of the solution to the half-space problem are presented.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811681","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
Exact Transport Coefficients from the Inelastic Rough Maxwell Model of a Granular Gas 粒状气体非弹性粗糙麦克斯韦模型的精确传输系数
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-27 DOI: 10.1007/s10955-024-03269-w
Andrés Santos, Gilberto M. Kremer
{"title":"Exact Transport Coefficients from the Inelastic Rough Maxwell Model of a Granular Gas","authors":"Andrés Santos,&nbsp;Gilberto M. Kremer","doi":"10.1007/s10955-024-03269-w","DOIUrl":"10.1007/s10955-024-03269-w","url":null,"abstract":"<div><p>Granular gases demand models capable of capturing their distinct characteristics. The widely employed inelastic hard-sphere model (IHSM) introduces complexities that are compounded when incorporating realistic features like surface roughness and rotational degrees of freedom, resulting in the more intricate inelastic rough hard-sphere model (IRHSM). This paper focuses on the inelastic rough Maxwell model (IRMM), presenting a more tractable alternative to the IRHSM and enabling exact solutions. Building on the foundation of the inelastic Maxwell model (IMM) applied to granular gases, the IRMM extends the mathematical representation to encompass surface roughness and rotational degrees of freedom. The primary objective is to provide exact expressions for the Navier–Stokes–Fourier transport coefficients within the IRMM, including the shear and bulk viscosities, the thermal and diffusive heat conductivities, and the cooling-rate transport coefficient. In contrast to earlier approximations in the IRHSM, our study unveils inherent couplings, such as shear viscosity to spin viscosity and heat conductivities to counterparts associated with a torque-vorticity vector. These exact findings provide valuable insights into refining the Sonine approximation applied to the IRHSM, contributing to a deeper understanding of the transport properties in granular gases with realistic features.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03269-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811434","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
Topological Expansive Lorenz Maps with a Hole at Critical Point 临界点有洞的拓扑扩展洛伦兹图
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-23 DOI: 10.1007/s10955-024-03265-0
Yun Sun, Bing Li, Yiming Ding
{"title":"Topological Expansive Lorenz Maps with a Hole at Critical Point","authors":"Yun Sun,&nbsp;Bing Li,&nbsp;Yiming Ding","doi":"10.1007/s10955-024-03265-0","DOIUrl":"10.1007/s10955-024-03265-0","url":null,"abstract":"<div><p>Let <i>f</i> be an expansive Lorenz map and <i>c</i> be the critical point. The survivor set is denoted as <span>(S_{f}(H):={xin [0,1]: f^{n}(x)notin H, forall nge 0})</span>, where <i>H</i> is an open subinterval. Here we study the hole <span>(H=(a,b))</span> with <span>(ale c le b)</span> and <span>(ane b )</span>. We observe that the case <span>(a=c)</span> is equivalent to the hole at 0, and the case <span>(b=c)</span> is equivalent to the hole at 1. Given any expansive Lorenz map <i>f</i> with a hole <span>(H=(a,b))</span> and <span>(S_{f}(H)nsubseteqq {0,1})</span>, we prove that there exists a Lorenz map <i>g</i> such that <span>(tilde{S}_{f}(H)setminus Omega (g))</span> is countable, where <span>(Omega (g))</span> is the Lorenz-shift of <i>g</i> and <span>(tilde{S}_{f}(H))</span> is the symbolic representation of <span>(S_{f}(H))</span>. Moreover, let <i>a</i> be fixed, we also give a complete characterization of the maximal plateau <i>I</i>(<i>b</i>) such that for all <span>(epsilon in I(b))</span>, <span>(S^+_{f}(a,epsilon )=S^+_{f}(a,b))</span>, and <i>I</i>(<i>b</i>) may degenerate to a single point <i>b</i>. As an application, when <i>f</i> has an ergodic acim and <i>a</i> is fixed, we obtain that the topological entropy function <span>(lambda _{f}(a):bmapsto h_{top}(f|S_{f}(a,b)))</span> is a devil staircase. At the special case that <i>f</i> being an intermediate <span>(beta )</span>-transformation, using the Ledrappier-Young formula, the Hausdorff dimension function <span>(eta _{f}(a):bmapsto dim _{mathcal {H}}(S_{f}(a,b)))</span> is naturally a devil staircase when fixing <i>a</i>. All the results can be naturally extended to the case that <i>b</i> is fixed. As a result, we extend the devil staircases in (Kalle et al. in Ergod Th Dyn Syst 40:2482–2514, 2020; Langeveld and Samuel in Acta Math Hungar 170:269–301, 2023; Urbanski in Ergod Th Dyn Syst 6:295–309, 1986) to expansive Lorenz maps with a hole at critical point.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800286","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 Energy in Spin Glass Models with Conventional Order 具有常规阶次的自旋玻璃模型中的自由能
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-15 DOI: 10.1007/s10955-024-03266-z
Hong-Bin Chen
{"title":"Free Energy in Spin Glass Models with Conventional Order","authors":"Hong-Bin Chen","doi":"10.1007/s10955-024-03266-z","DOIUrl":"10.1007/s10955-024-03266-z","url":null,"abstract":"<div><p>Recently, Baldwin and Swingle (J Stat Phys 190(7):125, 2023) considered spin glass models with additional conventional order parameters characterizing single-replica properties. These parameters are distinct from the standard order parameter, the overlap, used to measure correlations between replicas. A “min-max” formula for the free energy was prescribed in Baldwin and Swingle (2023). We rigorously verify this prescription in the setting of vector spin glass models featuring additional deterministic spin interactions. Notably, our results can be viewed as a generalization of the Parisi formula for vector spin glass models in Panchenko (Ann Probab 46(2):865–896, 2018), where the order parameter for self-overlap is already present.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586136","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
A Note on the Binding Energy for Bosons in the Mean-Field Limit 关于均场极限中玻色子束缚能的说明
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-06 DOI: 10.1007/s10955-024-03260-5
Lea Boßmann, Nikolai Leopold, David Mitrouskas, Sören Petrat
{"title":"A Note on the Binding Energy for Bosons in the Mean-Field Limit","authors":"Lea Boßmann,&nbsp;Nikolai Leopold,&nbsp;David Mitrouskas,&nbsp;Sören Petrat","doi":"10.1007/s10955-024-03260-5","DOIUrl":"10.1007/s10955-024-03260-5","url":null,"abstract":"<div><p>We consider a gas of <i>N</i> weakly interacting bosons in the ground state. Such gases exhibit Bose–Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic expansion for the binding energy, and compute the first orders explicitly for the homogeneous gas. Our result addresses in particular a conjecture by Nam (Lett Math Phys 108(1):141–159, 2018), and provides an asymptotic expansion of the ionization energy of bosonic atoms.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03260-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602303","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
Flocking Behavior of the Cucker–Smale Model on Infinite Graphs with a Central Vertex Group 有中心顶点群的无限图上卡克-斯马尔模型的成群行为
IF 1.3 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2024-04-06 DOI: 10.1007/s10955-024-03255-2
Xinyu Wang, Xiaoping Xue
{"title":"Flocking Behavior of the Cucker–Smale Model on Infinite Graphs with a Central Vertex Group","authors":"Xinyu Wang,&nbsp;Xiaoping Xue","doi":"10.1007/s10955-024-03255-2","DOIUrl":"10.1007/s10955-024-03255-2","url":null,"abstract":"<div><p>This article investigates the flocking behavior of the Cucker–Smale (CS) model on infinite graphs, considering both standard and cut-off interactions. We introduce the concept of connected infinite graphs with a central vertex group and then derive sufficient conditions for the CS model to produce flocking behavior. For standard interaction, we find that the CS model will exhibit flocking behavior exponentially when the connected infinite graph is equipped with a central vertex group. However, for cut-off interaction, we need the time-varying graph induced by interparticle distance to have a fixed central vertex group and the coupling strength to be above a certain threshold to produce the flocking behavior. Our theoretical analysis shows that if a connected infinite graph has a central vertex group, the second eigenvalue of the corresponding Laplacian is positive, which is crucial for the proof of flocking behavior. The consistent convergence towards flocking may well reveal the advantages and necessities of having a central vertex group in an infinite-particle complex system with sufficient intelligence.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140586210","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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