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XYZ Integrability the Easy Way XYZ可积性的简单方法
IF 1.1 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-19 DOI: 10.1007/s10955-026-03645-8
Paul Fendley, Sascha Gehrmann, Eric Vernier, Frank Verstraete
{"title":"XYZ Integrability the Easy Way","authors":"Paul Fendley,&nbsp;Sascha Gehrmann,&nbsp;Eric Vernier,&nbsp;Frank Verstraete","doi":"10.1007/s10955-026-03645-8","DOIUrl":"10.1007/s10955-026-03645-8","url":null,"abstract":"<div><p>Sutherland showed that the XYZ quantum spin-chain Hamiltonian commutes with the eight-vertex model transfer matrix, so that Baxter’s subsequent <i>tour de force</i> proves the integrability of both. The proof requires parametrising the Boltzmann weights using elliptic theta functions and showing they satisfy the Yang-Baxter equation. We here give a simpler derivation of the integrability of the XYZ chain by explicitly constructing an extensive sequence of conserved charges from a matrix-product operator. We show that they commute with the XYZ Hamiltonian with periodic boundary conditions or an arbitrary boundary magnetic field. A straightforward generalisation yields impurity interactions that preserve the integrability. Placing such an impurity at the edge gives an integrable generalisation of the Kondo problem with a gapped bulk. We make contact with the traditional approach by relating our matrix-product operator to products of the eight-vertex model transfer matrix.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03645-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281647","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
Quantum Filtering for Squeezed Noise Inputs 压缩噪声输入的量子滤波
IF 1.1 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-18 DOI: 10.1007/s10955-026-03644-9
John Gough, Dylon Rees
{"title":"Quantum Filtering for Squeezed Noise Inputs","authors":"John Gough,&nbsp;Dylon Rees","doi":"10.1007/s10955-026-03644-9","DOIUrl":"10.1007/s10955-026-03644-9","url":null,"abstract":"<div><p>We derive the quantum filter for a quantum open system undergoing quadrature measurements (homodyning) where the input field is in a general quasi-free state. This extends previous work for thermal input noise and allows for squeezed inputs. We introduce a convenient class of Bogoliubov transformations which we refer to as balanced and formulate the quantum stochastic model with squeezed noise as an Araki-Woods type representation. We make an essential use of the Tomita-Takesaki theory to construct the commutant of the C*-algebra describing the inputs and obtain the filtering equations using the quantum reference probability technique. The derived quantum filter must be independent of the choice of representation and this is achieved by fixing an independent quadrature in the commutant algebra.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03644-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261818","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
Long-Time Stability for the Nonlinear Quasi-Periodic Wave Equation on (mathbb {Z}^d) 非线性拟周期波动方程的长时间稳定性 (mathbb {Z}^d)
IF 1.1 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-18 DOI: 10.1007/s10955-026-03643-w
W.-M. Wang, Zhihan Zhang
{"title":"Long-Time Stability for the Nonlinear Quasi-Periodic Wave Equation on (mathbb {Z}^d)","authors":"W.-M. Wang,&nbsp;Zhihan Zhang","doi":"10.1007/s10955-026-03643-w","DOIUrl":"10.1007/s10955-026-03643-w","url":null,"abstract":"<div><p>For the discrete nonlinear quasi-periodic wave equation on <span>(mathbb {Z}^d)</span>, we establish the long-time stability of small-amplitude solutions. Although the perturbation lacks gauge invariance, we prove, via a partial normal form reduction, that the solutions remain localized for polynomially long times. Our result applies to the entire phase space, without restricting the number of active modes in the initial data, in particular, the initial data need not be finitely supported.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281411","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
Curvature-Based Multiscale Structural Contraction for Identifying Key Nodes in Complex Networks 基于曲率的多尺度结构收缩识别复杂网络中的关键节点
IF 1.1 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-17 DOI: 10.1007/s10955-026-03632-z
Jie Zhang, Hongbo Qu, Bo Song, Yu-Rong Song
{"title":"Curvature-Based Multiscale Structural Contraction for Identifying Key Nodes in Complex Networks","authors":"Jie Zhang,&nbsp;Hongbo Qu,&nbsp;Bo Song,&nbsp;Yu-Rong Song","doi":"10.1007/s10955-026-03632-z","DOIUrl":"10.1007/s10955-026-03632-z","url":null,"abstract":"<div><p>Identifying key nodes in complex networks is crucial for understanding their robustness and vulnerability. Nevertheless, this task remains an open and challenging problem. Traditional centrality measures often rely on single-scale topological information, which limits their ability to fully characterize node importance. To address this issue, this paper proposes a multiscale structural contraction method based on discrete curvature for key node identification. From a geometric perspective, discrete curvature is employed to quantify the tightness of connections between nodes guiding the iterative contraction of local structures and progressively constructing a multiscale representation of the network. By integrating structural information preserved across different scales and mapping the aggregated multiscale evaluation back to the original graph, a comprehensive ranking of node importance is generated. Experimental results demonstrate that the proposed method outperforms existing baseline approaches on both real-world and synthetic networks, enabling more accurate and robust identification of structurally critical nodes.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261775","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
Fokker-Planck Approach to Wave Turbulence 波湍流的福克-普朗克方法
IF 1.1 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-16 DOI: 10.1007/s10955-026-03639-6
Daniel Schubring
{"title":"Fokker-Planck Approach to Wave Turbulence","authors":"Daniel Schubring","doi":"10.1007/s10955-026-03639-6","DOIUrl":"10.1007/s10955-026-03639-6","url":null,"abstract":"<div><p>The Kolmogorov-Zakharov stationary states for weak wave turbulence involve solving a leading-order kinetic equation. Recent calculations of higher-order corrections to this kinetic equation using the Martin-Siggia-Rose path integral are reconsidered in terms of stationary states of a Fokker-Planck operator. A non-perturbative relation closely related to the quantum mechanical Ehrenfest theorem is introduced and used to express the kinetic equation in terms of divergences of two-point expectation values in the limit of zero dissipation. Similar equations are associated to divergences in higher-order cumulants. It is additionally shown that the ordinary thermal equilibrium state is not actually a stationary state of the Fokker-Planck operator, and a non-linear modification of dissipation is considered to remedy this.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261852","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
Recurrent Measures, Exponential Mixing and Limit Theorems for Stochastic Evolution Equations with Delay and Monotone Coefficients 具有延迟和单调系数的随机演化方程的循环测度、指数混合和极限定理
IF 1.1 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-15 DOI: 10.1007/s10955-026-03634-x
Shuaishuai Lu, Xue Yang, Yong Li
{"title":"Recurrent Measures, Exponential Mixing and Limit Theorems for Stochastic Evolution Equations with Delay and Monotone Coefficients","authors":"Shuaishuai Lu,&nbsp;Xue Yang,&nbsp;Yong Li","doi":"10.1007/s10955-026-03634-x","DOIUrl":"10.1007/s10955-026-03634-x","url":null,"abstract":"<div><p>We investigate a class of stochastic evolution equations with monotone coefficients and finite delay, motivated by non-equilibrium physical systems in which both memory effects and stochastic perturbations play essential roles. The inherent non-Markovian nature induced by delay challenges the application of classical ergodic theory. To overcome this challenge, we introduce the concept of recurrent entrance measures, which extends the classical notion of invariant measures to non-autonomous settings. By generalizing Shcherbakov’s comparability principle to a stochastic variational framework, we prove that these measures inherit the full spectrum of recurrence properties (e.g., stationary, periodic, quasi-periodic, almost periodic, Levitan almost periodic, Bohr almost automorphic, pseudo-periodic, Birkhoff recurrent, pseudo-recurrent and Poisson stable) from the system’s coefficients, marking a shift from pathwise to statistical descriptions of recurrence. For autonomous systems, we prove uniform exponential mixing in the Wasserstein metric and further establish strong laws of large numbers and central limit theorems for solution maps. Our results provide a unified statistical framework for stochastic evolution systems with delay, with applications to physical models exhibiting memory and stochastic forcing.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 6","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281166","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
Matrix-Product State Skeletons in Onsager-Integrable Quantum Chains onsager -可积量子链中的矩阵-积态骨架。
IF 1.1 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-15 DOI: 10.1007/s10955-026-03637-8
Imogen Camp, Nick G. Jones
{"title":"Matrix-Product State Skeletons in Onsager-Integrable Quantum Chains","authors":"Imogen Camp,&nbsp;Nick G. Jones","doi":"10.1007/s10955-026-03637-8","DOIUrl":"10.1007/s10955-026-03637-8","url":null,"abstract":"<div><p>Matrix-product state (MPS) skeletons are connected networks of Hamiltonians with exact MPS ground states that underlie a phase diagram. Such skeletons have previously been found in classes of free-fermion models. For the translation-invariant BDI and AIII free-fermion classes, it has been shown that the underlying skeleton is dense, giving an analytic approach to MPS approximation of ground states anywhere in the class. In this paper, we partially expose the skeleton in certain interacting spin chains: the <i>N</i>-state Onsager-integrable chiral clock families. We construct MPS that form a dense MPS skeleton in the gapped regions surrounding a sequence of fixed-point Hamiltonians (the generators of the Onsager algebra). Outside these gapped regions, these MPS remain eigenstates, but no longer give the many-body ground state. Rather, they are ground states in particular sectors of the spectrum. Our methods also allow us to find further MPS eigenstates; these correspond to low-lying excited states within the aforementioned gapped regions. This set of MPS excited states goes beyond the previous analysis of ground states on the <span>(N=2)</span> free-fermion MPS skeleton. As an application of our results, we find a closed form for the disorder parameter in a family of interacting models. Finally, we remark that many of our results use only the Onsager algebra and are not specific to the chiral clock model representation.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 6","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13269555/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148269615","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
Ergodicity, KAM, FPUT
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-12 DOI: 10.1007/s10955-026-03624-z
Giovanni Gallavotti
{"title":"Ergodicity, KAM, FPUT","authors":"Giovanni Gallavotti","doi":"10.1007/s10955-026-03624-z","DOIUrl":"10.1007/s10955-026-03624-z","url":null,"abstract":"<div><p>Boltzmann introduced the microcanonical ensemble in 1868, [1], and immediately attempted to give an example of a system whose stationary states would be described by the ensemble (as suggested also by his ergodic hypothesis). The example, [2], has been recently shown to be incorrect, if taken literally: the point was to suppose that constants of motion, if any besides the energy, would necessarily be smooth functions; and soon later he warned on the dangers implicit in a similar assumption. Fifty years later Fermi wrote a paper attempting to prove that in general a nonlinear system should be ergodic, [3]: but his proof relied again on Boltzmann’s assumption. Thirty-four more years elapsed, and Fermi returned on the problem collaborating with Pasta, Ulam, Tsingou: the surprise was that the considered non linear chain was apparently not following the ergodic hypothesis. In the same year Kolmogorov had proved the conservation of many quasi periodic motions in nonlinear perturbations of integrable systems, [4]: his theorem was considered, already a few years later, a possible explanation of the FPUT work, [5]. This was only the beginning of intense research: here a brief sketch is presented to illustrate the above themes and the connection with the multiscale aspects of the problems, and the “Renormalization group method” intended as a map <span>(mathcal R)</span> whose iterations can be interpreted as successive magnifications, zooming on ever smaller regions of phase space in which motions develop closer and closer to the searched quasi periodic motion of given spectrum.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03624-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148237297","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
Ground State Excitations and Energy Fluctuations in Short-Range Spin Glasses 短程自旋玻璃中的基态激发和能量涨落
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-08 DOI: 10.1007/s10955-026-03631-0
C. M. Newman, D. L. Stein
{"title":"Ground State Excitations and Energy Fluctuations in Short-Range Spin Glasses","authors":"C. M. Newman,&nbsp;D. L. Stein","doi":"10.1007/s10955-026-03631-0","DOIUrl":"10.1007/s10955-026-03631-0","url":null,"abstract":"<div><p>We study the stability of ground states in the Edwards-Anderson Ising spin glass in dimensions two and higher against perturbations of a single coupling. After reviewing the concepts of critical droplets, flexibilities and metastates, we show that, in any dimension, a certain kind of critical droplet with space-filling (i.e., positive spatial density) boundary does not exist in ground states generated by coupling-independent boundary conditions. Using this we show that if incongruent ground states exist in any dimension, the variance of their energy difference restricted to finite volumes scales proportionally to the volume. This in turn is used to prove that a metastate generated by (e.g.) periodic boundary conditions is unique and supported on a single pair of spin-reversed ground states in two dimensions. We further show that any excitation above an infinite-volume ground state with a positive-density interface must have the property that its energy difference with the ground state in a restricted volume diverges as the square root of the restricted volume.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03631-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236597","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
Cutoff Phenomenon for Inhomogeneous Nonlinear Recombination in Arbitrary Finite Product Spaces 任意有限积空间中非齐次非线性复合的截止现象
IF 1.2 3区 物理与天体物理
Journal of Statistical Physics Pub Date : 2026-06-08 DOI: 10.1007/s10955-026-03640-z
Junho Kim, Insuk Seo
{"title":"Cutoff Phenomenon for Inhomogeneous Nonlinear Recombination in Arbitrary Finite Product Spaces","authors":"Junho Kim,&nbsp;Insuk Seo","doi":"10.1007/s10955-026-03640-z","DOIUrl":"10.1007/s10955-026-03640-z","url":null,"abstract":"<div><p>In this article, we prove the cutoff phenomenon for a general class of the discrete-time nonlinear recombination models. This system models the evolution of a probability measure on a finite product space <span>(S^n)</span> representing the state of spins on <i>n</i> sites. Although its stationary distribution has a product structure, and its evolution is Markovian, the dynamics of the model is nonlinear. Consequently, the estimation of the <i>mixing time</i> becomes a highly non-trivial task. The special case with two spins and homogeneous stationary measure was considered in Caputo, Labbé, and Lacoin [The Annals of Applied Probability 35:1164–1197, 2025], where the cutoff phenomenon for the mixing behavior has been verified. In this article, we extend this result to the general case with finite spins and inhomogeneous stationary measure by developing a novel algebraic representation for the density fluctuation of the system with respect to its stationary state.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148236682","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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