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Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities 广义 MIT 袋模型的非相对论极限与光谱不等式。
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-07-22 DOI: 10.1007/s11040-024-09484-x
Jussi Behrndt, Dale Frymark, Markus Holzmann, Christian Stelzer-Landauer
{"title":"Nonrelativistic Limit of Generalized MIT Bag Models and Spectral Inequalities","authors":"Jussi Behrndt,&nbsp;Dale Frymark,&nbsp;Markus Holzmann,&nbsp;Christian Stelzer-Landauer","doi":"10.1007/s11040-024-09484-x","DOIUrl":"10.1007/s11040-024-09484-x","url":null,"abstract":"<div><p>For a family of self-adjoint Dirac operators <span>(-i c (alpha cdot nabla ) + frac{c^2}{2})</span> subject to generalized MIT bag boundary conditions on domains in <span>(mathbb {R}^3)</span>, it is shown that the nonrelativistic limit in the norm resolvent sense is the Dirichlet Laplacian. This allows to transfer spectral geometry results for Dirichlet Laplacians to Dirac operators for large <i>c</i>.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11263450/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141756480","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
On the Resolvent of H+A(^{*})+A 论 H+A $$^{*}$ +A 的溶剂
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-07-01 DOI: 10.1007/s11040-024-09481-0
Andrea Posilicano
{"title":"On the Resolvent of H+A(^{*})+A","authors":"Andrea Posilicano","doi":"10.1007/s11040-024-09481-0","DOIUrl":"10.1007/s11040-024-09481-0","url":null,"abstract":"<div><p>We present a much shorter and streamlined proof of an improved version of the results previously given in [A. Posilicano: On the Self-Adjointness of <span>(H+A^{*}+A)</span>. <i>Math. Phys. Anal. Geom.</i> <b>23</b> (2020)] concerning the self-adjoint realizations of formal QFT-like Hamiltonians of the kind <span>(H+A^{*}+A)</span>, where <i>H</i> and <i>A</i> play the role of the free field Hamiltonian and of the annihilation operator respectively. We give explicit representations of the resolvent and of the self-adjointness domain; the consequent Kreĭn-type resolvent formula leads to a characterization of these self-adjoint realizations as limit (with respect to convergence in norm resolvent sense) of cutoff Hamiltonians of the kind <span>(H+A^{*}_{n}+A_{n}-E_{n})</span>, the bounded operator <span>(E_{n})</span> playing the role of a renormalizing counter term. These abstract results apply to various concrete models in Quantum Field Theory.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09481-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141529824","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
Fluctuation Moments for Regular Functions of Wigner Matrices 维格纳矩阵正则函数的波动矩。
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-06-20 DOI: 10.1007/s11040-024-09483-y
Jana Reker
{"title":"Fluctuation Moments for Regular Functions of Wigner Matrices","authors":"Jana Reker","doi":"10.1007/s11040-024-09483-y","DOIUrl":"10.1007/s11040-024-09483-y","url":null,"abstract":"<div><p>We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of Male et al. (Random Matrices Theory Appl. 11(2):2250015, 2022), showing that the underlying combinatorics of non-crossing partitions and annular non-crossing permutations continue to stay valid beyond the setting of second-order free probability theory. The formulas obtained further characterize the variance in the functional central limit theorem given in the recent companion paper (Reker in Preprint, arXiv:2204.03419, 2023). and thus allow identifying the fluctuation around the thermal value in certain thermalization problems.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11190022/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141441930","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
Generating Function of q- and Elliptic Multiple Polylogarithms of Hurwitz Type 赫尔维茨型 q 多项式和椭圆多项式的生成函数
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-05-21 DOI: 10.1007/s11040-024-09480-1
Masaki Kato
{"title":"Generating Function of q- and Elliptic Multiple Polylogarithms of Hurwitz Type","authors":"Masaki Kato","doi":"10.1007/s11040-024-09480-1","DOIUrl":"10.1007/s11040-024-09480-1","url":null,"abstract":"<div><p>Ohno and Zagier (Indag Math 12:483–487, 2001) found that a generating function of sums of multiple polylogarithms can be written in terms of the Gauss hypergeometric function <span>({}_2F_1)</span>. As a generalization of the Ohno and Zagier formula, Ihara et al. (Can J Math 76:1–17, 2022) showed that a generating function of sums of interpolated multiple polylogarithms of Hurwitz type can be expressed in terms of the generalized hypergeometric function <span>({}_{r+1}F_r)</span>. In this paper, we establish <i>q</i>- and elliptic analogues of this result. We introduce elliptic <i>q</i>-multiple polylogarithms of Hurwitz type and study a generating function of sums of them. By taking the trigonometric and classical limits in the main theorem, we can obtain <i>q</i>- and elliptic generalizations of the Ihara, Kusunoki, Nakamura and Saeki formula.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09480-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141116516","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
Quasi-free Isomorphisms of Second Quantization Algebras and Modular Theory 二次量子化代数的准无同构与模块理论
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-04-23 DOI: 10.1007/s11040-024-09479-8
Roberto Conti, Gerardo Morsella
{"title":"Quasi-free Isomorphisms of Second Quantization Algebras and Modular Theory","authors":"Roberto Conti,&nbsp;Gerardo Morsella","doi":"10.1007/s11040-024-09479-8","DOIUrl":"10.1007/s11040-024-09479-8","url":null,"abstract":"<div><p>Using Araki–Yamagami’s characterization of quasi-equivalence for quasi-free representations of the CCRs, we provide an abstract criterion for the existence of isomorphisms of second quantization local von Neumann algebras induced by Bogolubov transformations in terms of the respective one particle modular operators. We discuss possible applications to the problem of local normality of vacua of Klein-Gordon fields with different masses.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09479-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140804510","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
Space-Time Fluctuations in a Quasi-static Limit 准静态极限中的时空波动
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-04-03 DOI: 10.1007/s11040-023-09474-5
Cédric Bernardin, Patricia Gonçalves, Stefano Olla
{"title":"Space-Time Fluctuations in a Quasi-static Limit","authors":"Cédric Bernardin,&nbsp;Patricia Gonçalves,&nbsp;Stefano Olla","doi":"10.1007/s11040-023-09474-5","DOIUrl":"10.1007/s11040-023-09474-5","url":null,"abstract":"<div><p>We consider the macroscopic limit for the space-time density fluctuations in the open symmetric simple exclusion in the quasi-static scaling limit. We prove that the distribution of these fluctuations converge to a gaussian space-time field that is delta correlated in time but with long-range correlations in space.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140560688","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
Cover Times of the Massive Random Walk Loop Soup 大规模随机漫步循环汤的覆盖时间
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-03-22 DOI: 10.1007/s11040-024-09478-9
Erik I. Broman, Federico Camia
{"title":"Cover Times of the Massive Random Walk Loop Soup","authors":"Erik I. Broman,&nbsp;Federico Camia","doi":"10.1007/s11040-024-09478-9","DOIUrl":"10.1007/s11040-024-09478-9","url":null,"abstract":"<div><p>We study cover times of subsets of <span>({mathbb {Z}}^2)</span> by a two-dimensional massive random walk loop soup. We consider a sequence of subsets <span>(A_n subset {mathbb {Z}}^2)</span> such that <span>(|A_n| rightarrow infty )</span> and determine the distributional limit of their cover times <span>({mathcal {T}}(A_n))</span>. We allow the killing rate <span>(kappa _n)</span> (or equivalently the “mass”) of the loop soup to depend on the size of the set <span>(A_n)</span> to be covered. In particular, we determine the limiting behavior of the cover times for inverse killing rates all the way up to <span>(kappa _n^{-1}=|A_n|^{1-8/(log log |A_n|)},)</span> showing that it can be described by a Gumbel distribution. Since a typical loop in this model will have length at most of order <span>(kappa _n^{-1/2}=|A_n|^{1/2},)</span> if <span>(kappa _n^{-1})</span> exceeded <span>(|A_n|,)</span> the cover times of all points in a tightly packed set <span>(A_n)</span> (i.e., a square or close to a ball) would presumably be heavily correlated, complicating the analysis. Our result comes close to this extreme case.\u0000</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11040-024-09478-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203039","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
Discrete, Continuous and Asymptotic for a Modified Singularly Gaussian Unitary Ensemble and the Smallest Eigenvalue of Its Large Hankel Matrices 修正奇异高斯单元集合的离散、连续和渐近及其大汉克尔矩阵的最小特征值
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-03-02 DOI: 10.1007/s11040-024-09477-w
Dan Wang, Mengkun Zhu
{"title":"Discrete, Continuous and Asymptotic for a Modified Singularly Gaussian Unitary Ensemble and the Smallest Eigenvalue of Its Large Hankel Matrices","authors":"Dan Wang,&nbsp;Mengkun Zhu","doi":"10.1007/s11040-024-09477-w","DOIUrl":"10.1007/s11040-024-09477-w","url":null,"abstract":"<div><p>This paper focuses on the characteristics of the Hankel determinant generated by a modified singularly Gaussian weight. The weight function is defined as: </p><div><div><span>$$begin{aligned} w(z;t)=|z|^{alpha }textrm{e}^{-frac{1}{z^2}-tleft( z^2-frac{1}{z^2}right) }, ~zin {mathbb {R}}, end{aligned}$$</span></div></div><p>where <span>(alpha &gt;1)</span> and <span>(tin (0,1))</span> are parameters. Using ladder operator techniques, we derive a series of difference formulas for the auxiliary quantities and recurrence coefficients. We present the difference equations for the recurrence coefficients and the logarithmic derivative of the Hankel determinant. We then use the “t-dependence\" to obtain the differential identities satisfied by the auxiliary quantities and the logarithmic derivative of the Hankel determinant. To obtain the large <i>n</i> asymptotic expressions of the recurrence coefficients, we use the Coulomb fluid method together with the related difference equations, which depend on <i>n</i> either being odd or even. We also obtain the reduction forms of the second-order differential equations satisfied by the orthogonal polynomials generated by this weight. Two special cases coincide with the bi-confluent Heun equation and the double confluent Heun equation, respectively. Finally, we calculate the asymptotic behavior of the smallest eigenvalue of large Hankel matrices generated by this weight. Our result not only covers the classical result of Szegö (Trans Am Math Soc 40:450–461, 1936) but also determines our next research direction.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019413","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
On the KPZ Scaling and the KPZ Fixed Point for TASEP 关于 KPZ 比例和 TASEP 的 KPZ 固定点
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-01-29 DOI: 10.1007/s11040-024-09475-y
Yuta Arai
{"title":"On the KPZ Scaling and the KPZ Fixed Point for TASEP","authors":"Yuta Arai","doi":"10.1007/s11040-024-09475-y","DOIUrl":"10.1007/s11040-024-09475-y","url":null,"abstract":"<div><p>We consider all totally asymmetric simple exclusion processes (TASEPs) whose transition probabilities are given by the Schütz-type formulas and which jump with homogeneous rates. We show that the multi-point distribution of particle positions and the KPZ scaling are described using the probability generating function of the rightmost particle’s jump. For all TASEPs satisfying certain assumptions, we also prove the pointwise convergence of the kernels appearing in the joint distribution of particle positions to those appearing in the KPZ fixed point formula. Our result generalizes the result of Matetski, Quastel, and Remenik [18] in the sense that we provide the KPZ fixed point formulation for a class of TASEPs, instead of for one specific TASEP.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646134","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
On the Integrable Structure of Deformed Sine Kernel Determinants 论变形正弦核决定因素的积分结构
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-01-27 DOI: 10.1007/s11040-024-09476-x
Tom Claeys, Sofia Tarricone
{"title":"On the Integrable Structure of Deformed Sine Kernel Determinants","authors":"Tom Claeys,&nbsp;Sofia Tarricone","doi":"10.1007/s11040-024-09476-x","DOIUrl":"10.1007/s11040-024-09476-x","url":null,"abstract":"<div><p>We study a family of Fredholm determinants associated to deformations of the sine kernel, parametrized by a weight function <i>w</i>. For a specific choice of <i>w</i>, this kernel describes bulk statistics of finite temperature free fermions. We establish a connection between these determinants and a system of integro-differential equations generalizing the fifth Painlevé equation, and we show that they allow us to solve an integrable PDE explicitly for a large class of initial data.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139582011","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
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