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Two-Term Asymptotics of the Exchange Energy of the Electron Gas on Symmetric Polytopes in the High-Density Limit 高密度极限对称多面体上电子气体交换能的两期渐近线
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-09-16 DOI: 10.1007/s11040-024-09485-w
Thiago Carvalho Corso
{"title":"Two-Term Asymptotics of the Exchange Energy of the Electron Gas on Symmetric Polytopes in the High-Density Limit","authors":"Thiago Carvalho Corso","doi":"10.1007/s11040-024-09485-w","DOIUrl":"https://doi.org/10.1007/s11040-024-09485-w","url":null,"abstract":"<p>We derive a two-term asymptotic expansion for the exchange energy of the free electron gas on strictly tessellating polytopes and fundamental domains of lattices in the thermodynamic limit. This expansion comprises a bulk (volume-dependent) term, the celebrated Dirac exchange, and a novel surface correction stemming from a boundary layer and finite-size effects. Furthermore, we derive analogous two-term asymptotic expansions for semi-local density functionals. By matching the coefficients of these asymptotic expansions, we obtain an integral constraint for semi-local approximations of the exchange energy used in density functional theory.\u0000</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266372","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
A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model 旋子随机偏微分方程的微局部研究及对瑟林模型的应用
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-08-28 DOI: 10.1007/s11040-024-09488-7
Alberto Bonicelli, Beatrice Costeri, Claudio Dappiaggi, Paolo Rinaldi
{"title":"A Microlocal Investigation of Stochastic Partial Differential Equations for Spinors with an Application to the Thirring Model","authors":"Alberto Bonicelli, Beatrice Costeri, Claudio Dappiaggi, Paolo Rinaldi","doi":"10.1007/s11040-024-09488-7","DOIUrl":"https://doi.org/10.1007/s11040-024-09488-7","url":null,"abstract":"<p>On a <i>d</i>-dimensional Riemannian, spin manifold (<i>M</i>, <i>g</i>) we consider non-linear, stochastic partial differential equations for spinor fields, driven by a Dirac operator and coupled to an additive Gaussian, vector-valued white noise. We extend to the case in hand a procedure, introduced in Dappiaggi et al (Commun Contemp Math 27(07):2150075, 2022), for the scalar counterpart, which allows to compute at a perturbative level the expectation value of the solutions as well as the associated correlation functions accounting intrinsically for the underlying renormalization freedoms. This framework relies strongly on tools proper of microlocal analysis and it is inspired by the algebraic approach to quantum field theory. As a concrete example we apply it to a stochastic version of the Thirring model proving in particular that it lies in the subcritical regime if <span>(dle 2)</span>.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201173","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
Limiting Spectral Distribution of Random Self-Adjoint Quantum Channels 随机自相邻量子信道的极限谱分布
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-08-05 DOI: 10.1007/s11040-024-09482-z
Cécilia Lancien, Patrick Oliveira Santos, Pierre Youssef
{"title":"Limiting Spectral Distribution of Random Self-Adjoint Quantum Channels","authors":"Cécilia Lancien, Patrick Oliveira Santos, Pierre Youssef","doi":"10.1007/s11040-024-09482-z","DOIUrl":"https://doi.org/10.1007/s11040-024-09482-z","url":null,"abstract":"<p>We study the limiting spectral distribution of quantum channels whose Kraus operators sampled as <span>( ntimes n)</span> random Hermitian matrices satisfying certain assumptions. We show that when the Kraus rank goes to infinity with <i>n</i>, the limiting spectral distribution (suitably rescaled) of the corresponding quantum channel coincides with the semi-circle distribution. When the Kraus rank is fixed, the limiting spectral distribution is no longer the semi-circle distribution. It corresponds to an explicit law, which can also be described using tools from free probability.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141947268","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
Møller Maps for Dirac Fields in External Backgrounds 外部背景中狄拉克场的默勒图
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-07-24 DOI: 10.1007/s11040-024-09487-8
Valentino Abram, Romeo Brunetti
{"title":"Møller Maps for Dirac Fields in External Backgrounds","authors":"Valentino Abram, Romeo Brunetti","doi":"10.1007/s11040-024-09487-8","DOIUrl":"https://doi.org/10.1007/s11040-024-09487-8","url":null,"abstract":"<p>In this paper we study the foundations of the algebraic treatment of classical and quantum field theories for Dirac fermions under external backgrounds following the initial contributions already present in various places in the literature. The treatment is restricted to contractible spacetimes of globally hyperbolic nature in dimensions <span>(dge 4)</span> and to external fields modelled with trivial principal bundles. In particular, we construct the classical Møller maps intertwining the configuration spaces of <i>charged</i> and <i>uncharged</i> fermions, and we show some of its properties in the case of a <i>U</i>(1) gauge charge. In the last part, as a first step towards a quantization of the theory, we explore the combination of the classical Møller maps with Hadamard bidistributions and prove that they are involutive isomorphisms (algebraically and topologically) between suitable (formal) algebras of functionals (observables) over the configuration spaces of charged and uncharged Dirac fields.</p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141779536","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 Riemann Curvature of Spherically Symmetric Metrics 论球面对称度量的黎曼曲率
IF 0.9 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-07-04 DOI: 10.1007/s11040-024-09486-9
S. G. Elgendi
{"title":"On Riemann Curvature of Spherically Symmetric Metrics","authors":"S. G. Elgendi","doi":"10.1007/s11040-024-09486-9","DOIUrl":"https://doi.org/10.1007/s11040-024-09486-9","url":null,"abstract":"","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141837422","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 Resolvent of H+A $$^{*}$$ +A 论 H+A $$^{*}$ +A 的溶剂
IF 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-07-01 DOI: 10.1007/s11040-024-09481-0
Andrea Posilicano
{"title":"On the Resolvent of H+A $$^{*}$$ +A","authors":"Andrea Posilicano","doi":"10.1007/s11040-024-09481-0","DOIUrl":"https://doi.org/10.1007/s11040-024-09481-0","url":null,"abstract":"<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>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-05-21 DOI: 10.1007/s11040-024-09480-1
Masakimi Kato
{"title":"Generating Function of q- and Elliptic Multiple Polylogarithms of Hurwitz Type","authors":"Masakimi Kato","doi":"10.1007/s11040-024-09480-1","DOIUrl":"https://doi.org/10.1007/s11040-024-09480-1","url":null,"abstract":"","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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 1 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, Gerardo Morsella","doi":"10.1007/s11040-024-09479-8","DOIUrl":"https://doi.org/10.1007/s11040-024-09479-8","url":null,"abstract":"<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>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","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 1 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, Patricia Gonçalves, Stefano Olla","doi":"10.1007/s11040-023-09474-5","DOIUrl":"https://doi.org/10.1007/s11040-023-09474-5","url":null,"abstract":"<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>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"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 1 3区 数学
Mathematical Physics, Analysis and Geometry Pub Date : 2024-03-22 DOI: 10.1007/s11040-024-09478-9
{"title":"Cover Times of the Massive Random Walk Loop Soup","authors":"","doi":"10.1007/s11040-024-09478-9","DOIUrl":"https://doi.org/10.1007/s11040-024-09478-9","url":null,"abstract":"<h3>Abstract</h3> <p>We study cover times of subsets of <span> <span>({mathbb {Z}}^2)</span> </span> by a two-dimensional massive random walk loop soup. We consider a sequence of subsets <span> <span>(A_n subset {mathbb {Z}}^2)</span> </span> such that <span> <span>(|A_n| rightarrow infty )</span> </span> and determine the distributional limit of their cover times <span> <span>({mathcal {T}}(A_n))</span> </span>. We allow the killing rate <span> <span>(kappa _n)</span> </span> (or equivalently the “mass”) of the loop soup to depend on the size of the set <span> <span>(A_n)</span> </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> <span>(kappa _n^{-1}=|A_n|^{1-8/(log log |A_n|)},)</span> </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> <span>(kappa _n^{-1/2}=|A_n|^{1/2},)</span> </span> if <span> <span>(kappa _n^{-1})</span> </span> exceeded <span> <span>(|A_n|,)</span> </span> the cover times of all points in a tightly packed set <span> <span>(A_n)</span> </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. </p>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","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":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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