Letters in Mathematical Physics最新文献_第7页

Correction: Volume singularities in general relativity 更正：广义相对论中的体积奇点

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s11005-024-01838-4

Leonardo García-Heveling

引用次数: 0

Long-time asymptotics for a complex cubic Camassa–Holm equation 复立方卡马萨-霍尔姆方程的长时渐近线

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1007/s11005-024-01833-9

Hongyi Zhang, Yufeng Zhang, Binlu Feng

{"title":"Long-time asymptotics for a complex cubic Camassa–Holm equation","authors":"Hongyi Zhang, Yufeng Zhang, Binlu Feng","doi":"10.1007/s11005-024-01833-9","DOIUrl":"10.1007/s11005-024-01833-9","url":null,"abstract":"<div>In this paper, we investigate the Cauchy problem of the following complex cubic Camassa–Holm equation <div><div>$$begin{aligned} m_{t}=bu_{x}+frac{1}{2}left[ mleft( |u|^{2}-left| u_{x}right| ^{2}right) right] _{x}-frac{1}{2} mleft( u bar{u}_{x}-u_{x} bar{u}right) , quad m=u-u_{x x}, end{aligned}$$</div></div>where (b>0) is an arbitrary positive real constant. Long-time asymptotics of the equation is obtained through the (bar{partial })-steepest descent method. Firstly, based on the spectral analysis of the Lax pair and scattering matrix, the solution of the equation is able to be constructed via solving the corresponding Riemann–Hilbert problem. Then, we present different long-time asymptotic expansions of the solution u(y, t) in different space-time solitonic regions of (xi =y/t). The half-plane ({(y,t):-infty<y< infty , t > 0}) is divided into four asymptotic regions: (xi in (-infty ,-1)), (xi in (-1,0)), (xi in (0,frac{1}{8})) and (xi in (frac{1}{8},+infty )). When (xi ) falls in ((-infty ,-1)cup (frac{1}{8},+infty )), no stationary phase point of the phase function (theta (z)) exists on the jump profile in the space-time region. In this case, corresponding asymptotic approximations can be characterized with an (N(Lambda ))-solitons with diverse residual error order (O(t^{-1+2varepsilon })). There are four stationary phase points and eight stationary phase points on the jump curve as (xi in (-1,0)) and (xi in (0,frac{1}{8})), respectively. The corresponding asymptotic form is accompanied by a residual error order (O(t^{-frac{3}{4}})).</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512721","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

Vertex operators of the KP hierarchy and singular algebraic curves KP 层次的顶点算子和奇异代数曲线

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-19 DOI: 10.1007/s11005-024-01836-6

Atsushi Nakayashiki

引用次数: 0

Attractor flow versus Hesse flow in wall-crossing structures 穿墙结构中的吸引流与黑塞流

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-08 DOI: 10.1007/s11005-024-01830-y

Qiang Wang

引用次数: 0

Usefulness of signed eigenvalue/vector distributions of random tensors 随机张量的符号特征值/向量分布的用途

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-07 DOI: 10.1007/s11005-024-01825-9

Max Regalado Kloos, Naoki Sasakura

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Non-local relativistic (delta )-shell interactions 非局部相对论 $$delta $$hell 相互作用

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-07 DOI: 10.1007/s11005-024-01828-6

Lukáš Heriban, Matěj Tušek

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Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups p-adic Lie 群上的不变度量：p-adic 四元数代数和 p-adic 旋转群上的哈尔积分

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-06 DOI: 10.1007/s11005-024-01826-8

Paolo Aniello, Sonia L’Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter

{"title":"Invariant measures on p-adic Lie groups: the p-adic quaternion algebra and the Haar integral on the p-adic rotation groups","authors":"Paolo Aniello, Sonia L’Innocente, Stefano Mancini, Vincenzo Parisi, Ilaria Svampa, Andreas Winter","doi":"10.1007/s11005-024-01826-8","DOIUrl":"10.1007/s11005-024-01826-8","url":null,"abstract":"<div>We provide a general expression of the Haar measure—that is, the essentially unique translation-invariant measure—on a p-adic Lie group. We then argue that this measure can be regarded as the measure naturally induced by the invariant volume form on the group, as it happens for a standard Lie group over the reals. As an important application, we next consider the problem of determining the Haar measure on the p-adic special orthogonal groups in dimension two, three and four (for every prime number p). In particular, the Haar measure on (text {SO}(2,mathbb {Q}_p)) is obtained by a direct application of our general formula. As for (text {SO}(3,mathbb {Q}_p)) and (text {SO}(4,mathbb {Q}_p)), instead, we show that Haar integrals on these two groups can conveniently be lifted to Haar integrals on certain p-adic Lie groups from which the special orthogonal groups are obtained as quotients. This construction involves a suitable quaternion algebra over the field (mathbb {Q}_p) and is reminiscent of the quaternionic realization of the real rotation groups. Our results should pave the way to the development of harmonic analysis on the p-adic special orthogonal groups, with potential applications in p-adic quantum mechanics and in the recently proposed p-adic quantum information theory.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-024-01826-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141512801","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 optimal error exponents for classical and quantum antidistinguishability 论经典和量子反区分性的最佳误差指数

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-05 DOI: 10.1007/s11005-024-01821-z

Hemant K. Mishra, Michael Nussbaum, Mark M. Wilde

{"title":"On the optimal error exponents for classical and quantum antidistinguishability","authors":"Hemant K. Mishra, Michael Nussbaum, Mark M. Wilde","doi":"10.1007/s11005-024-01821-z","DOIUrl":"10.1007/s11005-024-01821-z","url":null,"abstract":"<div>The concept of antidistinguishability of quantum states has been studied to investigate foundational questions in quantum mechanics. It is also called quantum state elimination, because the goal of such a protocol is to guess which state, among finitely many chosen at random, the system is not prepared in (that is, it can be thought of as the first step in a process of elimination). Antidistinguishability has been used to investigate the reality of quantum states, ruling out (psi )-epistemic ontological models of quantum mechanics (Pusey et al. in Nat Phys 8(6):475–478, 2012). Thus, due to the established importance of antidistinguishability in quantum mechanics, exploring it further is warranted. In this paper, we provide a comprehensive study of the optimal error exponent—the rate at which the optimal error probability vanishes to zero asymptotically—for classical and quantum antidistinguishability. We derive an exact expression for the optimal error exponent in the classical case and show that it is given by the multivariate classical Chernoff divergence. Our work thus provides this divergence with a meaningful operational interpretation as the optimal error exponent for antidistinguishing a set of probability measures. For the quantum case, we provide several bounds on the optimal error exponent: a lower bound given by the best pairwise Chernoff divergence of the states, a single-letter semi-definite programming upper bound, and lower and upper bounds in terms of minimal and maximal multivariate quantum Chernoff divergences. It remains an open problem to obtain an explicit expression for the optimal error exponent for quantum antidistinguishability.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"114 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259535","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

Zhelobenko–Stern formulas and (B_n) Toda wave functions 柘洛宾科-斯特恩公式和$B_n$$户田波函数

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-05 DOI: 10.1007/s11005-024-01824-w

A. Galiullin, S. Khoroshkin, M. Lyachko

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Generic spectrum of the weighted Laplacian operator on Cayley graphs Cayley 图上加权拉普拉斯算子的通用谱

IF 1.3 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2024-06-04 DOI: 10.1007/s11005-024-01827-7

Cristian F. Coletti, Lucas R. de Lima, Diego S. de Oliveira, Marcus A. M. Marrocos

引用次数: 0