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Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution 多临界舒尔量和特雷西-维多姆分布的高阶类似物
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-01-25 DOI: 10.1007/s11040-023-09472-7
Dan Betea, Jérémie Bouttier, Harriet Walsh
{"title":"Multicritical Schur Measures and Higher-Order Analogues of the Tracy–Widom Distribution","authors":"Dan Betea,&nbsp;Jérémie Bouttier,&nbsp;Harriet Walsh","doi":"10.1007/s11040-023-09472-7","DOIUrl":"10.1007/s11040-023-09472-7","url":null,"abstract":"<div><p>We introduce multicritical Schur measures, which are probability laws on integer partitions which give rise to non-generic fluctuations at their edge. They are in the same universality classes as one-dimensional momentum-space models of free fermions in flat confining potentials, studied by Le Doussal, Majumdar and Schehr. These universality classes involve critical exponents of the form <span>(1/(2m+1))</span>, with <i>m</i> a positive integer, and asymptotic distributions given by Fredholm determinants constructed from higher order Airy kernels, extending the generic Tracy–Widom GUE distribution recovered for <span>(m=1)</span>. We also compute limit shapes for the multicritical Schur measures, discuss the finite temperature setting, and exhibit an exact mapping to the multicritical unitary matrix models previously encountered by Periwal and Shevitz.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139581744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tau-Function of the Multi-component CKP Hierarchy 多组分 CKP 层次结构的 Tau 功能
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-01-02 DOI: 10.1007/s11040-023-09473-6
A. Zabrodin
{"title":"Tau-Function of the Multi-component CKP Hierarchy","authors":"A. Zabrodin","doi":"10.1007/s11040-023-09473-6","DOIUrl":"10.1007/s11040-023-09473-6","url":null,"abstract":"<div><p>We consider multi-component Kadomtsev-Petviashvili hierarchy of type C (the multi-component CKP hierarchy) originally defined with the help of matrix pseudo-differential operators via the Lax-Sato formalism. Starting from the bilinear relation for the wave functions, we prove existence of the tau-function for the multi-component CKP hierarchy and provide a formula which expresses the wave functions through the tau-function. We also find how this tau-function is related to the tau-function of the multi-component Kadomtsev-Petviashvili hierarchy. The tau-function of the multi-component CKP hierarchy satisfies an integral relation which, unlike the integral relation for the latter tau-function, is no longer bilinear but has a more complicated form.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139084228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Complex Creation Operator and Planar Automorphic Functions 复生成算子与平面自同构函数
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-11-01 DOI: 10.1007/s11040-023-09471-8
Ghanmi Allal, Imlal Lahcen
{"title":"Complex Creation Operator and Planar Automorphic Functions","authors":"Ghanmi Allal,&nbsp;Imlal Lahcen","doi":"10.1007/s11040-023-09471-8","DOIUrl":"10.1007/s11040-023-09471-8","url":null,"abstract":"<div><p>We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell–Humbert automorphy factor, arising as images of the holomorphic ones by means of the creation differential operator. This is closely connected to the spectral theory of the magnetic Laplacian on the complex plane.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795352","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Surgery Transformations and Spectral Estimates of (delta ) Beam Operators (delta )光束算子的手术变换和谱估计
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-10-17 DOI: 10.1007/s11040-023-09470-9
Aftab Ali, Muhammad Usman
{"title":"Surgery Transformations and Spectral Estimates of (delta ) Beam Operators","authors":"Aftab Ali,&nbsp;Muhammad Usman","doi":"10.1007/s11040-023-09470-9","DOIUrl":"10.1007/s11040-023-09470-9","url":null,"abstract":"<div><p>We introduce <span>(delta )</span> type vertex conditions for beam operators, the fourth-order differential operator, on finite, compact and connected metric graphs. Our study the effect of certain geometrical alterations (graph surgery) of the graph on their spectra. Results are obtained for a class of vertex conditions which can be seen as an analogue of <span>(delta )</span>-conditions for graphs Laplacian. There are a number of possible candidates of <span>(delta )</span> type conditions for beam operators. We develop surgery principles and record the monotonicity properties of their spectrum, keeping in view the possibility that vertex conditions may change within the same class after certain graph alterations. We also demonstrate the applications of surgery principles by obtaining several lower and upper estimates on the eigenvalues.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cohomology of Lie Algebra Morphism Triples and Some Applications 李代数态射三元组的上同调及其一些应用
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-09-25 DOI: 10.1007/s11040-023-09468-3
Apurba Das
{"title":"Cohomology of Lie Algebra Morphism Triples and Some Applications","authors":"Apurba Das","doi":"10.1007/s11040-023-09468-3","DOIUrl":"10.1007/s11040-023-09468-3","url":null,"abstract":"<div><p>A Lie algebra morphism triple is a triple <span>((mathfrak {g}, mathfrak {h}, phi ))</span> consisting of two Lie algebras <span>(mathfrak {g}, mathfrak {h})</span> and a Lie algebra homomorphism <span>(phi : mathfrak {g} rightarrow mathfrak {h})</span>. We define representations and cohomology of Lie algebra morphism triples. As applications of our cohomology, we study some aspects of deformations, abelian extensions of Lie algebra morphism triples and classify skeletal sh Lie algebra morphism triples. Finally, we consider the cohomology of Lie group morphism triples and find a relation with the cohomology of Lie algebra morphism triples.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve (y=x^{n}) 用代数曲线分离的不连续分段线性微分系统的第16 Hilbert问题 (y=x^{n})
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-09-19 DOI: 10.1007/s11040-023-09467-4
Jaume Llibre, Claudia Valls
{"title":"The 16th Hilbert Problem for Discontinuous Piecewise Linear Differential Systems Separated by the Algebraic Curve (y=x^{n})","authors":"Jaume Llibre,&nbsp;Claudia Valls","doi":"10.1007/s11040-023-09467-4","DOIUrl":"10.1007/s11040-023-09467-4","url":null,"abstract":"<div><p>We consider planar piecewise discontinuous differential systems formed by either linear centers or linear Hamiltonian saddles and separated by the algebraic curve <span>(y=x^n)</span> with <span>(n ge 2)</span>. We provide in a very short way an upper bound of the number of limit cycles that these differential systems can have in terms of <i>n</i>, proving the extended 16th Hilbert problem in this case. In particular, we show that for <span>(n=2)</span> this bound can be reached.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09467-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"7183673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Inverse Spectral Map for Dimers 二聚体的逆光谱图
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-09-12 DOI: 10.1007/s11040-023-09466-5
T. George, A. B. Goncharov, R. Kenyon
{"title":"The Inverse Spectral Map for Dimers","authors":"T. George,&nbsp;A. B. Goncharov,&nbsp;R. Kenyon","doi":"10.1007/s11040-023-09466-5","DOIUrl":"10.1007/s11040-023-09466-5","url":null,"abstract":"<div><p>In 2015, Vladimir Fock proved that the spectral transform, associating to an element of a dimer cluster integrable system its spectral data, is birational by constructing an inverse map using theta functions on Jacobians of spectral curves. We provide an alternate construction of the inverse map that involves only rational functions in the spectral data.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Integrable Systems of Finite Type from F-Cohomological Field Theories Without Unit 无单位F-同调场论中的有限型可积系统
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-09-09 DOI: 10.1007/s11040-023-09463-8
Alexandr Buryak, Danil Gubarevich
{"title":"Integrable Systems of Finite Type from F-Cohomological Field Theories Without Unit","authors":"Alexandr Buryak,&nbsp;Danil Gubarevich","doi":"10.1007/s11040-023-09463-8","DOIUrl":"10.1007/s11040-023-09463-8","url":null,"abstract":"<div><p>One of many manifestations of a deep relation between the topology of the moduli spaces of algebraic curves and the theory of integrable systems is a recent construction of Arsie, Lorenzoni, Rossi, and the first author associating an integrable system of evolutionary PDEs to an F-cohomological field theory (F-CohFT), which is a collection of cohomology classes on the moduli spaces of curves satisfying certain natural splitting properties. Typically, these PDEs have an infinite expansion in the dispersive parameter, which happens because they involve contributions from the moduli spaces of curves of arbitrarily large genus. In this paper, for each rank <span>(Nge 2)</span>, we present a family of F-CohFTs without unit, for which the equations of the associated integrable system have a finite expansion in the dispersive parameter. For <span>(N=2)</span>, we explicitly compute the primary flows of this integrable system.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43705195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k k阶Cayley树上Ising模型的一些非周期p进广义Gibbs测度
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-08-31 DOI: 10.1007/s11040-023-09465-6
Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev
{"title":"Some Non-periodic p-Adic Generalized Gibbs Measures for the Ising Model on a Cayley Tree of Order k","authors":"Muzaffar Rahmatullaev,&nbsp;Akbarkhuja Tukhtabaev","doi":"10.1007/s11040-023-09465-6","DOIUrl":"10.1007/s11040-023-09465-6","url":null,"abstract":"<div><p>In the present paper, we consider a <i>p</i>-adic Ising model on a Cayley tree. The existence of non-periodic <i>p</i>-adic generalized Gibbs measures of this model is investigated. In particular, we construct <i>p</i>-adic analogue of the Bleher–Ganikhodjaev construction and generalize some constructive methods. Moreover, the boundedness of obtained measures are established, which yields the occurrence of a phase transition.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42039520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Relative Entropy of Fermion Excitation States on the CAR Algebra CAR代数上费米子激发态的相对熵
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2023-08-30 DOI: 10.1007/s11040-023-09464-7
Stefano Galanda, Albert Much, Rainer Verch
{"title":"Relative Entropy of Fermion Excitation States on the CAR Algebra","authors":"Stefano Galanda,&nbsp;Albert Much,&nbsp;Rainer Verch","doi":"10.1007/s11040-023-09464-7","DOIUrl":"10.1007/s11040-023-09464-7","url":null,"abstract":"<div><p>The relative entropy of certain states on the algebra of canonical anticommutation relations (CAR) is studied in the present work. The CAR algebra is used to describe fermionic degrees of freedom in quantum mechanics and quantum field theory. The states for which the relative entropy is investigated are multi-excitation states (similar to multi-particle states) with respect to KMS states defined with respect to a time-evolution induced by a unitary dynamical group on the one-particle Hilbert space of the CAR algebra. If the KMS state is quasifree, the relative entropy of multi-excitation states can be explicitly calculated in terms of 2-point functions, which are defined entirely by the one-particle Hilbert space defining the CAR algebra and the Hamilton operator of the dynamical group on the one-particle Hilbert space. This applies also in the case that the one-particle Hilbert space Hamilton operator has a continuous spectrum so that the relative entropy of multi-excitation states cannot be defined in terms of von Neumann entropies. The results obtained here for the relative entropy of multi-excitation states on the CAR algebra can be viewed as counterparts of results for the relative entropy of coherent states on the algebra of canonical commutation relations which have appeared recently. It turns out to be useful to employ the setting of a self-dual CAR algebra introduced by Araki.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-023-09464-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47859155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
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