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Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-30 DOI: 10.1007/s11005-025-01901-8
Vladimir Lotoreichik
{"title":"Inequalities between Dirichlet and Neumann eigenvalues of the magnetic Laplacian","authors":"Vladimir Lotoreichik","doi":"10.1007/s11005-025-01901-8","DOIUrl":"10.1007/s11005-025-01901-8","url":null,"abstract":"<div><p>We consider the magnetic Laplacian with the homogeneous magnetic field in two and three dimensions. We prove that the <span>((k+1))</span>-th magnetic Neumann eigenvalue of a bounded convex planar domain is not larger than its <i>k</i>-th magnetic Dirichlet eigenvalue for all <span>(kin {{mathbb {N}}})</span>. In three dimensions, we restrict our attention to convex domains, which are invariant under rotation by an angle of <span>(pi )</span> around an axis parallel to the magnetic field. For such domains, we prove that the <span>((k+2))</span>-th magnetic Neumann eigenvalue is not larger than the <i>k</i>-th magnetic Dirichlet eigenvalue provided that this Dirichlet eigenvalue is simple. The proofs rely on a modification of the strategy suggested by Payne and developed further by Levine and Weinberger.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01901-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110070","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
Loschmidt echo for deformed Wigner matrices
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-30 DOI: 10.1007/s11005-025-01904-5
László Erdős, Joscha Henheik, Oleksii Kolupaiev
{"title":"Loschmidt echo for deformed Wigner matrices","authors":"László Erdős,&nbsp;Joscha Henheik,&nbsp;Oleksii Kolupaiev","doi":"10.1007/s11005-025-01904-5","DOIUrl":"10.1007/s11005-025-01904-5","url":null,"abstract":"<div><p>We consider two Hamiltonians that are close to each other, <span>(H_1 approx H_2 )</span>, and analyze the time decay of the corresponding <i>Loschmidt echo</i> <span>(mathfrak {M}(t):= |langle psi _0, textrm{e}^{textrm{i} t H_2} textrm{e}^{-textrm{i} t H_1} psi _0 rangle |^2)</span> that expresses the effect of an imperfect time reversal on the initial state <span>(psi _0)</span>. Our model Hamiltonians are deformed Wigner matrices that do not share a common eigenbasis. The main tools are new two-resolvent laws for such <span>(H_1)</span> and <span>(H_2)</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11782466/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143078413","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
New combinatorial formulae for nested Bethe vectors II
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s11005-025-01896-2
Maksim Kosmakov, Vitaly Tarasov
{"title":"New combinatorial formulae for nested Bethe vectors II","authors":"Maksim Kosmakov,&nbsp;Vitaly Tarasov","doi":"10.1007/s11005-025-01896-2","DOIUrl":"10.1007/s11005-025-01896-2","url":null,"abstract":"<div><p>We give new combinatorial formulae for vector-valued weight functions (off-shell nested Bethe vectors) for the evaluation modules over the Yangian <span>(Y(mathfrak {gl}_n))</span>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11775048/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143063015","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
Investigations of warped product manifolds through the concircular curvature tensor with relativistic applications
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s11005-025-01900-9
Abdallah Abdelhameed Syied, Crina Daniela Neacşu, Nasser Bin Turki, Gabriel-Eduard Vîlcu
{"title":"Investigations of warped product manifolds through the concircular curvature tensor with relativistic applications","authors":"Abdallah Abdelhameed Syied,&nbsp;Crina Daniela Neacşu,&nbsp;Nasser Bin Turki,&nbsp;Gabriel-Eduard Vîlcu","doi":"10.1007/s11005-025-01900-9","DOIUrl":"10.1007/s11005-025-01900-9","url":null,"abstract":"<div><p>This article focuses on characterizing warped product manifolds through the flatness and the symmetry of the concircular curvature tensor. It is proved that the factor manifolds of a concircularly-flat warped product manifold have constant sectional curvatures as well as they are concircularly-flat. It is shown that in a concircularly-symmetric warped product manifold, the fiber manifold has constant sectional curvature and it is concircularly-flat, while the base manifold is locally-symmetric and concircularly-symmetric. It is demonstrated that a concircularly-flat (symmetric) GRW space-time is perfect fluid and static. Finally, it is established that in a concircularly-flat (symmetric) <i>F</i>-associated standard static space-time, the base manifold has constant sectional curvature and it is concircularly-flat, while the fiber manifold is locally-symmetric and concircularly-symmetric.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01900-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109564","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
Tetrahedron instantons on orbifolds
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-28 DOI: 10.1007/s11005-025-01903-6
Richard J. Szabo, Michelangelo Tirelli
{"title":"Tetrahedron instantons on orbifolds","authors":"Richard J. Szabo,&nbsp;Michelangelo Tirelli","doi":"10.1007/s11005-025-01903-6","DOIUrl":"10.1007/s11005-025-01903-6","url":null,"abstract":"<div><p>Given a homomorphism <span>(tau )</span> from a suitable finite group <span>({mathsf {Gamma }})</span> to <span>(textsf{SU}(4))</span> with image <span>({mathsf {Gamma }}^tau )</span>, we construct a cohomological gauge theory on a non-commutative resolution of the quotient singularity <span>(mathbbm {C}^4/{mathsf {Gamma }}^tau )</span> whose BRST fixed points are <span>({mathsf {Gamma }})</span>-invariant tetrahedron instantons on a generally non-effective orbifold. The partition function computes the expectation values of complex codimension one defect operators in rank <i>r</i> cohomological Donaldson–Thomas theory on a flat gerbe over the quotient stack <span>([mathbbm {C}^4/,{mathsf {Gamma }}^tau ])</span>. We describe the generalized ADHM parametrization of the tetrahedron instanton moduli space and evaluate the orbifold partition functions through virtual torus localization. If <span>({mathsf {Gamma }})</span> is an abelian group the partition function is expressed as a combinatorial series over arrays of <span>({mathsf {Gamma }})</span>-coloured plane partitions, while if <span>({mathsf {Gamma }})</span> is non-abelian the partition function localizes onto a sum over torus-invariant connected components of the moduli space labelled by lower-dimensional partitions. When <span>({mathsf {Gamma }}=mathbbm {Z}_n)</span> is a finite abelian subgroup of <span>(textsf{SL}(2,mathbbm {C}))</span>, we exhibit the reduction of Donaldson–Thomas theory on the toric Calabi–Yau four-orbifold <span>(mathbbm {C}^2/,{mathsf {Gamma }}times mathbbm {C}^2)</span> to the cohomological field theory of tetrahedron instantons, from which we express the partition function as a closed infinite product formula. We also use the crepant resolution correspondence to derive a closed formula for the partition function on any polyhedral singularity.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01903-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109565","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
On the relativistic quantum mechanics of a photon between two electrons in (1+1) dimensions
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-24 DOI: 10.1007/s11005-025-01898-0
Lawrence Frolov, Samuel Leigh, Shadi Tahvildar-Zadeh
{"title":"On the relativistic quantum mechanics of a photon between two electrons in (1+1) dimensions","authors":"Lawrence Frolov,&nbsp;Samuel Leigh,&nbsp;Shadi Tahvildar-Zadeh","doi":"10.1007/s11005-025-01898-0","DOIUrl":"10.1007/s11005-025-01898-0","url":null,"abstract":"<div><p>A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two electrons (or alternatively, two positrons). Manifest covariance is achieved using Dirac’s formalism of multi-time wave functions, i.e., wave functions <span>(Psi ({textbf {x}}_{text {ph}},{textbf {x}}_{text {e}_1},{textbf {x}}_{text {e}_2}))</span> where <span>({textbf {x}}_{text {ph}},{textbf {x}}_{text {e}_1},{textbf {x}}_{text {e}_2})</span> are generic spacetime events of the photon and two electrons, respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifolds <span>({{textbf {x}}_{text {ph}}={textbf {x}}_{text {e}_1}})</span> and <span>({{textbf {x}}_{text {ph}}={textbf {x}}_{text {e}_2}})</span> compatible with conservation of probability current. The corresponding initial-boundary value problem is shown to be well-posed, and it is shown that the unique solution can be represented by a convergent infinite sum of Feynman-like diagrams, each one corresponding to the photon bouncing between the two electrons a fixed number of times.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-025-01898-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109215","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 spectral (zeta )-function for quasi-regular Sturm–Liouville operators
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-22 DOI: 10.1007/s11005-024-01893-x
Guglielmo Fucci, Mateusz Piorkowski, Jonathan Stanfill
{"title":"The spectral (zeta )-function for quasi-regular Sturm–Liouville operators","authors":"Guglielmo Fucci,&nbsp;Mateusz Piorkowski,&nbsp;Jonathan Stanfill","doi":"10.1007/s11005-024-01893-x","DOIUrl":"10.1007/s11005-024-01893-x","url":null,"abstract":"<div><p>In this work, we analyze the spectral <span>(zeta )</span>-function associated with the self-adjoint extensions, <span>(T_{A,B})</span>, of quasi-regular Sturm–Liouville operators that are bounded from below. By utilizing the Green’s function formalism, we find the characteristic function, which implicitly provides the eigenvalues associated with a given self-adjoint extension <span>(T_{A,B})</span>. The characteristic function is then employed to construct a contour integral representation for the spectral <span>(zeta )</span>-function of <span>(T_{A,B})</span>. By assuming a general form for the asymptotic expansion of the characteristic function, we describe the analytic continuation of the <span>(zeta )</span>-function to a larger region of the complex plane. We also present a method for computing the value of the spectral <span>(zeta )</span>-function of <span>(T_{A,B})</span> at all positive integers. We provide two examples to illustrate the methods developed in the paper: the generalized Bessel and Legendre operators. We show that in the case of the generalized Bessel operator, the spectral <span>(zeta )</span>-function develops a branch point at the origin, while in the case of the Legendre operator it presents, more remarkably, branch points at every nonpositive integer value of <i>s</i>.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01893-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109015","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
High-frequency two-dimensional asymptotic standing coastal trapped waves in nearly integrable case 近可积情况下高频二维渐近驻岸困波
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-18 DOI: 10.1007/s11005-025-01895-3
Vladislav Rykhlov, Anatoly Anikin
{"title":"High-frequency two-dimensional asymptotic standing coastal trapped waves in nearly integrable case","authors":"Vladislav Rykhlov,&nbsp;Anatoly Anikin","doi":"10.1007/s11005-025-01895-3","DOIUrl":"10.1007/s11005-025-01895-3","url":null,"abstract":"<div><p>This paper continues the study of explicit asymptotic formulas for standing coastal trapped waves, focusing on the spectral properties of the operator <span>(langle nabla , D(x)nabla rangle )</span>, which is the spatial component of the wave operator with a degenerating wave propagation velocity. We aim to construct spectral series—pairs of asymptotic eigenvalues and formal asymptotic eigenfunctions—corresponding to the high-frequency regime, where the eigenvalue is <span>(varvec{omega }rightarrow infty )</span>. Extending earlier results, this study addresses the nearly integrable case, providing a more detailed asymptotic behavior of eigenfunctions. Depending on their domain of localization, these eigenfunctions can be expressed in terms of Airy functions and their derivatives or Bessel functions. In addition, we introduce a canonical operator with violated (imprecisely satisfied) quantization conditions.</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142994977","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 non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation painleve3方程sinh-Gordon约简奇异渐近性的非线性最陡下降方法
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-13 DOI: 10.1007/s11005-024-01892-y
Alexander R. Its, Kenta Miyahara, Maxim L. Yattselev
{"title":"The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation","authors":"Alexander R. Its,&nbsp;Kenta Miyahara,&nbsp;Maxim L. Yattselev","doi":"10.1007/s11005-024-01892-y","DOIUrl":"10.1007/s11005-024-01892-y","url":null,"abstract":"<div><p>Motivated by the simplest case of tt*-Toda equations, we study the large and small <i>x</i> asymptotics for <span>( x&gt;0 )</span> of real solutions of the sinh-Godron Painlevé III(<span>(D_6)</span>) equation. These solutions are parametrized through the monodromy data of the corresponding Riemann–Hilbert problem. This unified approach provides connection formulae between the behavior at the origin and infinity of the considered solutions.\u0000</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963066","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
Special issue honouring Mary Beth Ruskai 纪念玛丽·贝丝·鲁斯凯的特刊
IF 1.3 3区 物理与天体物理
Letters in Mathematical Physics Pub Date : 2025-01-04 DOI: 10.1007/s11005-024-01891-z
Andreas Winter, Bruno Nachtergaele, Matthias Christandl, Fumio Hiai, Graeme Smith, Simone Warzel
{"title":"Special issue honouring Mary Beth Ruskai","authors":"Andreas Winter,&nbsp;Bruno Nachtergaele,&nbsp;Matthias Christandl,&nbsp;Fumio Hiai,&nbsp;Graeme Smith,&nbsp;Simone Warzel","doi":"10.1007/s11005-024-01891-z","DOIUrl":"10.1007/s11005-024-01891-z","url":null,"abstract":"","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01891-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142925707","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
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