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Annales Henri Poincaré最新文献

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Wannier–Stark Localization for Time Quasi-Periodic Hamiltonian Operator on (mathbb {Z}) 上时间拟周期哈密顿算子的wanner - stark局部化 (mathbb {Z})
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2025-01-06 DOI: 10.1007/s00023-024-01533-z
Shengqing Hu, Yingte Sun
{"title":"Wannier–Stark Localization for Time Quasi-Periodic Hamiltonian Operator on (mathbb {Z})","authors":"Shengqing Hu,&nbsp;Yingte Sun","doi":"10.1007/s00023-024-01533-z","DOIUrl":"10.1007/s00023-024-01533-z","url":null,"abstract":"<div><p>In this paper, we consider the time (quasi)-periodic quantum Hamiltonian of the form <span>(textrm{H}(t)=textrm{H}_gamma +textrm{V}(omega t))</span>, where <span>(textrm{H}_gamma )</span> is a power-law long-range lattice operator with uniform electric fields on <span>(mathbb {Z})</span>, <span>(textrm{V}(omega t))</span> is a time quasi-periodic perturbation. In particular, we can obtain the uniform power-law localization of the Floquet Hamiltonian operator <span>(-{textbf{i}}omega cdot partial _{phi }+textrm{H}(phi ))</span>, and the dynamical localization of the Hamiltonian operator <span>(textrm{H}(t))</span>. No assumptions are made on the size of the perturbation; however, we require the time quasi-periodic perturbation is a <b>“quasi-Töplitz” operator</b> (close to a Töplitz operator).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 10","pages":"3739 - 3766"},"PeriodicalIF":1.3,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204684","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
Bessel Kernel Determinants and Integrable Equations 贝塞尔核行列式与可积方程
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2025-01-03 DOI: 10.1007/s00023-024-01527-x
Giulio Ruzza
{"title":"Bessel Kernel Determinants and Integrable Equations","authors":"Giulio Ruzza","doi":"10.1007/s00023-024-01527-x","DOIUrl":"10.1007/s00023-024-01527-x","url":null,"abstract":"<div><p>We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential equation describing isospectral deformations of a Sturm–Liouville equation. We also derive identities relating solutions to the integrable partial differential equation and to the Sturm–Liouville equation which imply an analogue for Painlevé V of Amir–Corwin–Quastel “integro-differential Painlevé II equation”. This equation reduces, in a degenerate limit, to the system of coupled Painlevé V equations derived by Charlier and Doeraene for the generating function of the Bessel process and to the Painlevé V equation derived by Tracy and Widom for the gap probability of the Bessel process. Finally, we study an initial value problem for the integrable partial differential equation. The approach is based on Its–Izergin–Korepin–Slavnov theory of integrable operators and their associated Riemann–Hilbert problems.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 6","pages":"2035 - 2068"},"PeriodicalIF":1.3,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161203","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
Prethermalization for Deformed Wigner Matrices 变形Wigner矩阵的预热化。
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-17 DOI: 10.1007/s00023-024-01518-y
László Erdős, Joscha Henheik, Jana Reker, Volodymyr Riabov
{"title":"Prethermalization for Deformed Wigner Matrices","authors":"László Erdős,&nbsp;Joscha Henheik,&nbsp;Jana Reker,&nbsp;Volodymyr Riabov","doi":"10.1007/s00023-024-01518-y","DOIUrl":"10.1007/s00023-024-01518-y","url":null,"abstract":"<div><p>We prove that a class of weakly perturbed Hamiltonians of the form <span>(H_lambda = H_0 + lambda W)</span>, with <i>W</i> being a Wigner matrix, exhibits <i>prethermalization</i>. That is, the time evolution generated by <span>(H_lambda )</span> relaxes to its ultimate thermal state via an intermediate prethermal state with a lifetime of order <span>(lambda ^{-2})</span>. Moreover, we obtain a general relaxation formula, expressing the perturbed dynamics via the unperturbed dynamics and the ultimate thermal state. The proof relies on a two-resolvent law for the deformed Wigner matrix <span>(H_lambda )</span>.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 6","pages":"1991 - 2033"},"PeriodicalIF":1.3,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12133972/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144236085","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
Relative Entropy and Mutual Information in Gaussian Statistical Field Theory 高斯统计场论中的相对熵和互信息
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-17 DOI: 10.1007/s00023-024-01522-2
Markus Schröfl, Stefan Floerchinger
{"title":"Relative Entropy and Mutual Information in Gaussian Statistical Field Theory","authors":"Markus Schröfl,&nbsp;Stefan Floerchinger","doi":"10.1007/s00023-024-01522-2","DOIUrl":"10.1007/s00023-024-01522-2","url":null,"abstract":"<div><p>Relative entropy is a powerful measure of the dissimilarity between two statistical field theories in the continuum. In this work, we study the relative entropy between Gaussian scalar field theories in a finite volume with different masses and boundary conditions. We show that the relative entropy depends crucially on <i>d</i>, the dimension of Euclidean space. Furthermore, we demonstrate that the mutual information between two disjoint regions in <span>(mathbb {R}^d)</span> is finite if the two regions are separated by a finite distance and satisfies an area law. We then construct an example of “touching” regions between which the mutual information is infinite. We argue that the properties of mutual information in scalar field theories can be explained by the Markov property of these theories.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 9","pages":"3233 - 3319"},"PeriodicalIF":1.3,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01522-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990641","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
Generalized Pentagon Equations 广义五边形方程
IF 1.4 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-16 DOI: 10.1007/s00023-024-01523-1
Anton Alekseev, Florian Naef, Muze Ren
{"title":"Generalized Pentagon Equations","authors":"Anton Alekseev,&nbsp;Florian Naef,&nbsp;Muze Ren","doi":"10.1007/s00023-024-01523-1","DOIUrl":"10.1007/s00023-024-01523-1","url":null,"abstract":"<div><p>Drinfeld defined the Knizhnik–Zamolodchikov (KZ) associator <span>(Phi _{textrm{KZ}})</span> by considering the regularized holonomy of the KZ connection along the <i>droit chemin</i> [0, 1]. The KZ associator is a group-like element of the free associative algebra with two generators, and it satisfies the pentagon equation. In this paper, we consider paths on <span>({mathbb {C}}backslash { z_1, dots , z_n})</span> which start and end at tangential base points. These paths are not necessarily straight, and they may have a finite number of transversal self-intersections. We show that the regularized holonomy <i>H</i> of the KZ connection associated with such a path satisfies a generalization of Drinfeld’s pentagon equation. In this equation, we encounter <i>H</i>, <span>(Phi _{textrm{KZ}})</span>, and new factors associated with self-intersections, tangential base points, and the rotation number of the path.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 3","pages":"877 - 894"},"PeriodicalIF":1.4,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01523-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143726655","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
KMS States on ({mathbb {Z}}_2)-Crossed Products and Twisted KMS Functionals ({mathbb {Z}}_2)上的KMS状态——交叉产品和扭曲的KMS功能
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-15 DOI: 10.1007/s00023-024-01516-0
Ricardo Correa da Silva, Johannes Große, Gandalf Lechner
{"title":"KMS States on ({mathbb {Z}}_2)-Crossed Products and Twisted KMS Functionals","authors":"Ricardo Correa da Silva,&nbsp;Johannes Große,&nbsp;Gandalf Lechner","doi":"10.1007/s00023-024-01516-0","DOIUrl":"10.1007/s00023-024-01516-0","url":null,"abstract":"<div><p>KMS states on <span>({mathbb {Z}}_2)</span>-crossed products of unital <span>(C^*)</span>-algebras <span>({mathcal {A}})</span> are characterized in terms of KMS states and twisted KMS functionals of <span>({mathcal {A}})</span>. These functionals are shown to describe the extensions of KMS states <span>(omega )</span> on <span>({mathcal {A}})</span> to the crossed product <span>({mathcal {A}} rtimes {mathbb {Z}}_2)</span> and can also be characterized by the twisted center of the von Neumann algebra generated by the GNS representation corresponding to <span>(omega )</span>. As a particular class of examples, KMS states on <span>({mathbb {Z}}_2)</span>-crossed products of CAR algebras with dynamics and grading given by Bogoliubov automorphisms are analyzed in detail. In this case, one or two extremal KMS states are found depending on a Gibbs-type condition involving the odd part of the absolute value of the Hamiltonian. As an application in mathematical physics, the extended field algebra of the Ising QFT is shown to be a <span>({mathbb {Z}}_2)</span>-crossed product of a CAR algebra which has a unique KMS state.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 11","pages":"4109 - 4139"},"PeriodicalIF":1.3,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01516-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145248332","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
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-14
{"title":"","authors":"","doi":"","DOIUrl":"","url":null,"abstract":"","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 10","pages":"3829 - 3870"},"PeriodicalIF":1.3,"publicationDate":"2024-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204683","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
Typical Macroscopic Long-Time Behavior for Random Hamiltonians 随机哈密顿量的典型宏观长时间行为
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-12 DOI: 10.1007/s00023-024-01521-3
Stefan Teufel, Roderich Tumulka, Cornelia Vogel
{"title":"Typical Macroscopic Long-Time Behavior for Random Hamiltonians","authors":"Stefan Teufel,&nbsp;Roderich Tumulka,&nbsp;Cornelia Vogel","doi":"10.1007/s00023-024-01521-3","DOIUrl":"10.1007/s00023-024-01521-3","url":null,"abstract":"<div><p>We consider a closed macroscopic quantum system in a pure state <span>(psi _t)</span> evolving unitarily and take for granted that different macro states correspond to mutually orthogonal subspaces <span>({mathcal {H}}_nu )</span> (macro spaces) of Hilbert space, each of which has large dimension. We extend previous work on the question what the evolution of <span>(psi _t)</span> looks like macroscopically, specifically on how much of <span>(psi _t)</span> lies in each <span>({mathcal {H}}_nu )</span>. Previous bounds concerned the <i>absolute</i> error for typical <span>(psi _0)</span> and/or <i>t</i> and are valid for arbitrary Hamiltonians <i>H</i>; now, we provide bounds on the <i>relative</i> error, which means much tighter bounds, with probability close to 1 by modeling <i>H</i> as a random matrix, more precisely as a random band matrix (i.e., where only entries near the main diagonal are significantly nonzero) in a basis aligned with the macro spaces. We exploit particularly that the eigenvectors of <i>H</i> are delocalized in this basis. Our main mathematical results confirm the two phenomena of generalized normal typicality (a type of long-time behavior) and dynamical typicality (a type of similarity within the ensemble of <span>(psi _0)</span> from an initial macro space). They are based on an extension we prove of a no-gaps delocalization result for random matrices by Rudelson and Vershynin (Geom Funct Anal 26:1716–1776, 2016).</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 9","pages":"3189 - 3231"},"PeriodicalIF":1.3,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01521-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144990429","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
Modular Hamiltonian for Fermions of Small Mass 小质量费米子的模哈密顿量
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-05 DOI: 10.1007/s00023-024-01508-0
Daniela Cadamuro, Markus B. Fröb, Christoph Minz
{"title":"Modular Hamiltonian for Fermions of Small Mass","authors":"Daniela Cadamuro,&nbsp;Markus B. Fröb,&nbsp;Christoph Minz","doi":"10.1007/s00023-024-01508-0","DOIUrl":"10.1007/s00023-024-01508-0","url":null,"abstract":"<div><p>We consider the algebra of massive fermions restricted to a diamond in two-dimensional Minkowski spacetime, and in the Minkowski vacuum state. While the massless modular Hamiltonian is known for this setting, the derivation of the massive one is an open problem. We compute the small-mass corrections to the modular Hamiltonian in a perturbative approach, finding some terms which were previously overlooked. Our approach can in principle be extended to all orders in the mass, even though it becomes computationally challenging.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 11","pages":"4071 - 4108"},"PeriodicalIF":1.3,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01508-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145248329","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
Slow Propagation Velocities in Schrödinger Operators with Large Periodic Potential 具有大周期势的Schrödinger算子的慢传播速度
IF 1.3 3区 物理与天体物理
Annales Henri Poincaré Pub Date : 2024-12-02 DOI: 10.1007/s00023-024-01520-4
Houssam Abdul-Rahman, Mohammed Darras, Christoph Fischbacher, Günter Stolz
{"title":"Slow Propagation Velocities in Schrödinger Operators with Large Periodic Potential","authors":"Houssam Abdul-Rahman,&nbsp;Mohammed Darras,&nbsp;Christoph Fischbacher,&nbsp;Günter Stolz","doi":"10.1007/s00023-024-01520-4","DOIUrl":"10.1007/s00023-024-01520-4","url":null,"abstract":"<div><p>Schrödinger operators with periodic potential have generally been shown to exhibit ballistic transport. In this work, we investigate whether the propagation velocity, while positive, can be made arbitrarily small by a suitable choice of the periodic potential. We consider the discrete one-dimensional Schrödinger operator <span>(Delta +mu V)</span>, where <span>(Delta )</span> is the discrete Laplacian, <i>V</i> is a <i>p</i>-periodic non-degenerate potential and <span>(mu &gt;0)</span>. We establish a Lieb–Robinson-type bound with a group velocity that scales like <span>(mathcal {O}(1/mu ))</span> as <span>(mu rightarrow infty )</span>. This shows the existence of a linear light cone with a maximum velocity of quantum propagation that is decaying at a rate proportional to <span>(1/mu )</span>. Furthermore, we prove that the asymptotic velocity, or the average velocity of the time-evolved state, exhibits a decay proportional to <span>(mathcal {O}(1/mu ^{p-1}))</span> as <span>(mu rightarrow infty )</span>.\u0000</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 10","pages":"3635 - 3663"},"PeriodicalIF":1.3,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145204688","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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