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Spectrum of Schrödinger operators on subcovering graphs 子覆盖图上Schrödinger算子的谱
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-07-16 DOI: 10.1007/s11005-025-01962-9
Natalia Saburova
{"title":"Spectrum of Schrödinger operators on subcovering graphs","authors":"Natalia Saburova","doi":"10.1007/s11005-025-01962-9","DOIUrl":"10.1007/s11005-025-01962-9","url":null,"abstract":"<div><p>We consider discrete Schrödinger operators with real periodic potentials on periodic graphs. The spectra of the operators consist of a finite number of bands. By \"rolling up\" a periodic graph along some appropriate directions we obtain periodic graphs of smaller dimensions called subcovering graphs. For example, rolling up a planar hexagonal lattice along different directions will lead to nanotubes with various chiralities. We describe connections between spectra of the Schrödinger operators on a periodic graph and its subcoverings. In particular, we provide a simple criterion for the subcovering graph to be isospectral to the original periodic graph. By isospectrality of periodic graphs we mean that the spectra of the Schrödinger operators on the graphs consist of the same number of bands and the corresponding bands coincide as sets. We also obtain asymptotics of the band edges of the Schrödinger operator on the subcovering graph as the \"chiral\" (roll up) vectors are long enough.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143584","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
Relative volume of comparable pairs under semigroup majorization 半群优化下可比较对的相对体积
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-07-14 DOI: 10.1007/s11005-025-01968-3
Fabio Deelan Cunden, Jakub Czartowski, Giovanni Gramegna, A. de Oliveira Junior
{"title":"Relative volume of comparable pairs under semigroup majorization","authors":"Fabio Deelan Cunden,&nbsp;Jakub Czartowski,&nbsp;Giovanni Gramegna,&nbsp;A. de Oliveira Junior","doi":"10.1007/s11005-025-01968-3","DOIUrl":"10.1007/s11005-025-01968-3","url":null,"abstract":"<div><p>Any semigroup <span>(mathcal {S})</span> of stochastic matrices induces a semigroup majorization relation <span>(prec ^{mathcal {S}})</span> on the set <span>(Delta _{n-1})</span> of probability <i>n</i>-vectors. Pick <i>X</i>, <i>Y</i> at random in <span>(Delta _{n-1})</span>: what is the probability that <i>X</i> and <i>Y</i> are comparable under <span>(prec ^{mathcal {S}})</span>? We review recent asymptotic (<span>(nrightarrow infty )</span>) results and conjectures in the case of <i>majorization</i> relation (when <span>(mathcal {S})</span> is the set of doubly stochastic matrices), discuss natural generalisations, and prove a new asymptotic result in the case of majorization, and new exact finite-<i>n</i> formulae in the case of <i>UT-majorization</i> relation, i.e. when <span>(mathcal {S})</span> is the set of upper-triangular stochastic matrices.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01968-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143532","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
Konno–Sato theorem for a covering of a graph 图的覆盖的Konno-Sato定理
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-07-12 DOI: 10.1007/s11005-025-01960-x
Iwao Sato, Takashi Komatsu, Norio Konno, Hideo Mitsuhashi
{"title":"Konno–Sato theorem for a covering of a graph","authors":"Iwao Sato,&nbsp;Takashi Komatsu,&nbsp;Norio Konno,&nbsp;Hideo Mitsuhashi","doi":"10.1007/s11005-025-01960-x","DOIUrl":"10.1007/s11005-025-01960-x","url":null,"abstract":"<div><p>The Grover matrix of a graph <i>G</i> is a typical time evolution matrix of a discrete-time quantum walk on <i>G</i>. We treat the Grover matrix of a finite covering of <i>G</i> and present a decomposition formula for the determinant of it. Furthermore, we define an <i>L</i>-function of a graph with respect to the Grover matrix and present its determinant expression. As a corollary, we express the determinant of the Grover matrix of a covering of <i>G</i> as a product of its <i>L</i>-functions.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143252","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
The Hecke-Baxter operators via Heisenberg group extensions Heisenberg群扩展的Hecke-Baxter算子
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-07-12 DOI: 10.1007/s11005-025-01971-8
A. A. Gerasimov, D. R. Lebedev, S. V. Oblezin
{"title":"The Hecke-Baxter operators via Heisenberg group extensions","authors":"A. A. Gerasimov,&nbsp;D. R. Lebedev,&nbsp;S. V. Oblezin","doi":"10.1007/s11005-025-01971-8","DOIUrl":"10.1007/s11005-025-01971-8","url":null,"abstract":"<div><p>The <span>(GL_{ell +1}(mathbb {R}))</span> Hecke-Baxter operator was introduced as an element of the <span>(O_{ell +1})</span>-spherical Hecke algebra associated with the Gelfand pair <span>(O_{ell +1}subset GL_{ell +1}(mathbb {R}))</span>. It was specified by the property to act on an <span>(O_{ell +1})</span>-fixed vector in a <span>(GL_{ell +1}(mathbb {R}))</span>-principal series representation via multiplication by the local Archimedean <i>L</i>-factor canonically attached to the representation. In this note we propose another way to define the Hecke-Baxter operator, identifying it with a generalized Whittaker function for an extension of the Lie group <span>(GL_{ell +1}(mathbb {R})times GL_{ell +1}(mathbb {R}))</span> by a Heisenberg Lie group. We also show how this Whittaker function can be lifted to a matrix element of an extension of the Lie group <span>(Sp_{2ell +2}(mathbb {R})times Sp_{2ell +2}(mathbb {R}))</span> by a Heisenberg Lie group.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143251","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
Quantum theory from classical mechanics near equilibrium 接近平衡的经典力学量子理论
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-06-28 DOI: 10.1007/s11005-025-01967-4
A. Schwarz
{"title":"Quantum theory from classical mechanics near equilibrium","authors":"A. Schwarz","doi":"10.1007/s11005-025-01967-4","DOIUrl":"10.1007/s11005-025-01967-4","url":null,"abstract":"<div><p>We consider classical theories described by Hamiltonians <i>H</i>(<i>p</i>, <i>q</i>) that have a non-degenerate minimum at the point where generalized momenta <i>p</i> and generalized coordinates <i>q</i> vanish. We assume that the sum of squares of generalized momenta and generalized coordinates is an integral of motion. In this situation, in the neighborhood of the point <span>(p=0, q=0)</span>, the quadratic part of a Hamiltonian plays a dominant role. We suppose that a classical observer can observe only physical quantities corresponding to quadratic Hamiltonians and show that in this case, he should conclude that the laws of quantum theory govern his world.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01967-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170064","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
Compatibility of Drinfeld presentations for split affine Kac–Moody quantum symmetric pairs 分裂仿射Kac-Moody量子对称对的Drinfeld表示的兼容性。
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-06-28 DOI: 10.1007/s11005-025-01964-7
Jian-Rong Li, Tomasz Przeździecki
{"title":"Compatibility of Drinfeld presentations for split affine Kac–Moody quantum symmetric pairs","authors":"Jian-Rong Li,&nbsp;Tomasz Przeździecki","doi":"10.1007/s11005-025-01964-7","DOIUrl":"10.1007/s11005-025-01964-7","url":null,"abstract":"<div><p>Let <span>((textbf{U}, textbf{U}^imath ))</span> be a split affine quantum symmetric pair of type <span>(textsf{B}_n^{(1)}, textsf{C}_n^{(1)})</span> or <span>(textsf{D}_n^{(1)})</span>. We prove factorization and coproduct formulae for the Drinfeld–Cartan operators <span>(Theta _i(z))</span> in the Lu–Wang Drinfeld-type presentation, generalizing the type <span>(textsf{A}_n^{(1)})</span> result from Przeździecki (arXiv:2311.13705). As an application, we show that a boundary analogue of the <i>q</i>-character map, defined via the spectra of these operators, is compatible with the usual <i>q</i>-character map. As an auxiliary result, we also produce explicit reduced expressions for the fundamental weights in the extended affine Weyl groups of classical types.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12206215/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144525912","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
Copositive geometry of Feynman integrals 费曼积分的共轭几何
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-06-27 DOI: 10.1007/s11005-025-01961-w
Bernd Sturmfels, Máté L. Telek
{"title":"Copositive geometry of Feynman integrals","authors":"Bernd Sturmfels,&nbsp;Máté L. Telek","doi":"10.1007/s11005-025-01961-w","DOIUrl":"10.1007/s11005-025-01961-w","url":null,"abstract":"<div><p>Copositive matrices and copositive polynomials are objects from optimization. We connect these to the geometry of Feynman integrals in physics. The integral is guaranteed to converge if its kinematic parameters lie in the copositive cone. Pólya’s method makes this manifest. We study the copositive cone for the second Symanzik polynomial of any Feynman graph. Its algebraic boundary is described by Landau discriminants.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01961-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170553","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
Nonperturbative refined topological string 非微扰精细拓扑弦
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-06-26 DOI: 10.1007/s11005-025-01965-6
Wu-yen Chuang
{"title":"Nonperturbative refined topological string","authors":"Wu-yen Chuang","doi":"10.1007/s11005-025-01965-6","DOIUrl":"10.1007/s11005-025-01965-6","url":null,"abstract":"<div><p>A formula for the full nonperturbative topological string free energy was recently proposed by Hattab and Palti (Non-perturbative topological string theory on compact Calabi-Yau manifolds from M-theory. arXiv:2408.09255 [hep-th]). In this work, we extend their result to the refined topological string theory. We demonstrate that the proposed formula for the full nonperturbative refined topological string free energy correctly reproduces the trans-series structure of the refined topological string and captures the Stokes automorphisms associated with its resurgent properties.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170282","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
Correction to: On the effect of derivative interactions in quantum field theory 修正：关于量子场论中导数相互作用的影响
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-06-26 DOI: 10.1007/s11005-025-01969-2
Karl-Henning Rehren
{"title":"Correction to: On the effect of derivative interactions in quantum field theory","authors":"Karl-Henning Rehren","doi":"10.1007/s11005-025-01969-2","DOIUrl":"10.1007/s11005-025-01969-2","url":null,"abstract":"","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01969-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170283","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
The zeta determinant of the reduced Lorentz group localized at a representation 约简洛伦兹群的行列式定域于一个表示
IF 1.4 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-06-25 DOI: 10.1007/s11005-025-01959-4
M. Spreafico
{"title":"The zeta determinant of the reduced Lorentz group localized at a representation","authors":"M. Spreafico","doi":"10.1007/s11005-025-01959-4","DOIUrl":"10.1007/s11005-025-01959-4","url":null,"abstract":"<div><p>We introduce some spectral functions on the reduced Lorentz group and on its spinor group localized at an irreducible unitary representation, and we study their main analytic properties. More precisely, we consider the trace of the heat operator and the spectral zeta function of the Hodge Laplace operator on functions. We show that the localized zeta function has a regular analytic extension with simple poles, and we find a closed formula for the zeta determinant of the localized Hodge Laplace operator. We give a closed formula for the trace of the (global) heat operator and we study its expansion for small time.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168794","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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