Letters in Mathematical Physics最新文献_第2页

Low-dimensional tori in Calogero–Moser–Sutherland systems Calogero-Moser-Sutherland系统中的低维环面

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1007/s11005-026-02072-w

Andrii Liashyk, Guorui Ma, Nicolai Reshetikhin, Ivan Sechin

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Ground state energy of a dilute Bose gas with three-body hard-core interactions 具有三体硬核相互作用的稀释玻色气体的基态能量

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1007/s11005-026-02067-7

Lukas Junge, François L. A. Visconti

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Mean-field limit from general mixtures of experts to quantum neural networks 从一般专家混合到量子神经网络的平均场极限

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-27 DOI: 10.1007/s11005-026-02065-9

Anderson Melchor Hernandez, Davide Pastorello, Giacomo De Palma

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More scaling limits for 1D random Schrödinger operators with critically decaying and vanishing potential 具有临界衰减和消失势的一维随机Schrödinger算子的更多缩放限制

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-26 DOI: 10.1007/s11005-026-02073-9

Yi Han

{"title":"More scaling limits for 1D random Schrödinger operators with critically decaying and vanishing potential","authors":"Yi Han","doi":"10.1007/s11005-026-02073-9","DOIUrl":"10.1007/s11005-026-02073-9","url":null,"abstract":"<div>Consider the random Schrödinger operator (H_n) defined on ({0,1,cdots ,n}subset mathbb {Z})<div><div>$$begin{aligned} (H_npsi )_ell =psi _{ell -1,n}+psi _{ell +1,n}+sigma frac{omega _ell }{a_{ell ,n}}psi _{ell ,n},quad psi _0=psi _{n+1}=0, end{aligned}$$</div></div>where (sigma >0), (omega _ell ) are i.i.d. random variables and (a_{ell ,n}) typically has order (sqrt{n}) for (ell in [epsilon n,(1-epsilon )n]) and any (epsilon >0). Two important cases: (a) the vanishing case (a_{ell ,n}=sqrt{n}) and (b) the decaying case (a_{ell ,n}=sqrt{ell }), were studied before in [1]. In this paper, we consider more general decaying profiles that lie in between these two extreme cases. We characterize the scaling limit of transfer matrices and determine the point process limit of eigenvalues near a fixed energy in the bulk, in terms of solutions to coupled SDEs. We obtain new point processes that share similar properties to the (text {Sch}_tau ) process. We determine the shape profile of eigenfunctions after a suitable rescaling that corresponds to a uniformly chosen eigenvalue of (H_n). We also give a more detailed description of the newly defined point processes, including the probability of small and large gaps and a variance estimate.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561862","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

A formula for the block expansion in free CFTs and applications to (mathcal{N}=4) SYM at strong coupling 自由CFTs中块膨胀的公式及其在(mathcal{N}=4) SYM强耦合中的应用

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-26 DOI: 10.1007/s11005-026-02070-y

F. Aprile, J. M. Drummond, P. J. Heslop, M. Santagata

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Modular resurgence, q-Pochhammer symbols, and quantum operators from mirror curves 模复现，q-Pochhammer符号，和镜像曲线的量子算子

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-25 DOI: 10.1007/s11005-026-02063-x

Veronica Fantini, Claudia Rella

{"title":"Modular resurgence, q-Pochhammer symbols, and quantum operators from mirror curves","authors":"Veronica Fantini, Claudia Rella","doi":"10.1007/s11005-026-02063-x","DOIUrl":"10.1007/s11005-026-02063-x","url":null,"abstract":"<div>Building on the results of [1, 2], we study the resurgence of q-Pochhammer symbols and determine their summability and quantum modularity properties. We construct a new, infinite family of pairs of modular resurgent series from the asymptotic expansions of sums of q-Pochhammer symbols weighted by suitable Dirichlet characters. These weighted sums fit into the modular resurgence paradigm and provide further evidence supporting our conjectures in [1]. In the context of the topological string/spectral theory correspondence for toric Calabi–Yau threefolds, Kashaev and Mariño proved that the spectral traces of canonical quantum operators associated with local weighted projective planes can be expressed as sums of q-Pochhammer symbols. Exploiting this relation, we show that an exact strong–weak resurgent symmetry, first observed by the second author in [3] and fully formalized in [2] for local ({mathbb {P}}^2), applies to all local (mathbb {P}^{m,n}), albeit stripped of some of the underlying number-theoretic properties. Under some assumptions, these properties are restored when considering linear combinations of the spectral traces that reproduce the weighted sums above.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561687","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

Riemann–Hilbert approach for a higher-order short pulse equation on the line 直线上高阶短脉冲方程的Riemann-Hilbert逼近

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-21 DOI: 10.1007/s11005-026-02066-8

Cong Lv, Q. P. Liu, Shoufeng Shen

{"title":"Riemann–Hilbert approach for a higher-order short pulse equation on the line","authors":"Cong Lv, Q. P. Liu, Shoufeng Shen","doi":"10.1007/s11005-026-02066-8","DOIUrl":"10.1007/s11005-026-02066-8","url":null,"abstract":"<div>This paper presents a Riemann–Hilbert (RH) approach to the inverse scattering transform, which is employed to solve the initial value problem for a higher-order short pulse (SP) equation on the line with zero boundary conditions. The RH problem is formulated for two types of scattering data: one with N simple poles and the other with N higher-order poles. Using the asymptotic behavior of the spectral variable at (k=0), the solution of the higher-order SP equation is recovered from the solution of the RH problem. In the reflectionless case, we generalize the residue theorem, which allows us to derive multiple higher-order pole solutions for the higher-order SP equation by solving a linear algebraic system. Finally, general formulae are derived for the solutions of the higher-order SP equation, which cover cases of N simple poles and N higher-order poles. As applications, explicit simple-pole and double-pole solutions are displayed in both analytical and graphical forms. Depending on the parameter choices, these correspond to singular-loop solitons and two distinct types of breathers.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560504","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

Fluctuations of Young diagrams for symplectic groups and semiclassical orthogonal polynomials 辛群与半经典正交多项式Young图的涨落

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-21 DOI: 10.1007/s11005-026-02068-6

Anton Nazarov, Anton Selemenchuk

{"title":"Fluctuations of Young diagrams for symplectic groups and semiclassical orthogonal polynomials","authors":"Anton Nazarov, Anton Selemenchuk","doi":"10.1007/s11005-026-02068-6","DOIUrl":"10.1007/s11005-026-02068-6","url":null,"abstract":"<div>Consider an (ntimes k) matrix of i.i.d. Bernoulli random numbers with (p=1/2). The dual RSK algorithm gives a bijection of this matrix to a pair of Young tableaux of conjugate shape, which is manifestation of skew Howe (GL_{n}times GL_{k})-duality. Thus the probability measure on zero–ones matrix leads to the probability measure on Young diagrams proportional to the ratio of the dimension of (GL_{n}times GL_{k})-representation and the dimension of the exterior algebra (bigwedge left( mathbb {C}^{n}otimes mathbb {C}^{k}right) ). Similarly, by applying Proctor’s algorithm based on Berele’s modification of the Schensted insertion, we get skew Howe duality for the pairs of groups (Sp_{2n}times Sp_{2k}). In the limit when (n,krightarrow infty ) (GL)-case is relatively easily studied by use of free-fermionic representation for the correlation kernel. But for the symplectic groups there is no convenient free-fermionic representation. We use Christoffel transformation to obtain the semiclassical orthogonal polynomials for (Sp_{2n}times Sp_{2k}) from Krawtchouk polynomials that describe (GL_{2n}times GL_{2k}) case. We derive an integral representation for semiclassical polynomials. The study of the asymptotic of this integral representation gives us the description of the limit shapes and fluctuations of the random Young diagrams for symplectic groups.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560505","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 zipper condition for 4-tensors in two-dimensional topological order and the higher relative commutants of a subfactor arising from a commuting square 二维拓扑序中4张量的拉链条件及由可交换方产生的子因子的高相对交换子

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-18 DOI: 10.1007/s11005-026-02069-5

Yasuyuki Kawahigashi

{"title":"The zipper condition for 4-tensors in two-dimensional topological order and the higher relative commutants of a subfactor arising from a commuting square","authors":"Yasuyuki Kawahigashi","doi":"10.1007/s11005-026-02069-5","DOIUrl":"10.1007/s11005-026-02069-5","url":null,"abstract":"<div>Researchers in condensed matter physics recently study two-dimensional topological order in terms of tensor networks involving certain 3- and 4-tensors. Their 3-tensors satisfying the “zipper condition” play an important role there, and such 3-tensors can be made into certain 2-tensors by combining two wires into one. We identify their 4-tensors with bi-unitary connections in Jones’ subfactor theory in operator algebras with precise normalization constants. Then we prove that their 2-tensors satisfying the zipper condition are the same as flat fields of strings in subfactor theory which correspond to elements in the higher relative commutants of the subfactor arising from the bi-unitary connection. This is what we expect, since the zipper condition is a kind of pentagon relations, but we clarify what conditions are exactly needed for this—we do not need the flatness or the finite depth condition for the bi-unitary connection. We actually generalize their 4-tensors so that the four index sets of the 4-tensors can be all different and work on a “half-version” of the zipper condition.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11005-026-02069-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559788","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 singularities of the spectral shift function for some tight-binding models 一些紧密结合模型的谱移函数的奇异性

IF 1.4 3区物理与天体物理

Letters in Mathematical Physics Pub Date : 2026-03-17 DOI: 10.1007/s11005-026-02060-0

M. Assal, O. Bourget, D. Sambou, A. Taarabt

{"title":"On the singularities of the spectral shift function for some tight-binding models","authors":"M. Assal, O. Bourget, D. Sambou, A. Taarabt","doi":"10.1007/s11005-026-02060-0","DOIUrl":"10.1007/s11005-026-02060-0","url":null,"abstract":"<div>We consider perturbed discrete tight-binding models in (ell ^2(mathbb {Z}_h,mathcal {G})) describing union of quantum particles with localized interactions, where (mathbb {Z}_h) is the 1D lattice (hmathbb {Z}), (h > 0), and (mathcal {G}) is a separable Hilbert space. The perturbations play the role of self-adjoint relatively compact (matrix-valued) electric potentials with (mathcal {B}(mathcal {G}))-valued coefficients decaying polynomially at infinity. We analyze the spectral shift function (SSF) associated with the pair of the perturbed and the unperturbed operators. On the one hand, we show that the SSF is bounded near the spectral thresholds of the essential spectrum if (dim (mathcal {G}) < +infty ). On the other hand, if (dim (mathcal {G}) = +infty ), we show that it may have singularities at some thresholds points (mu ) of the essential spectrum. In particular, new mechanisms allowing the SSF to have singularities at the thresholds are exhibited, based on the degeneracy of the spectrum of the unperturbed operator. Moreover, we give the main terms of the asymptotic behaviors of the SSF near (mu ) described in terms of some explicit effective Berezin–Toeplitz type operators. These results are completed by Levinson type formulas and examples of eigenvalues asymptotics for power-like and exponential decay potentials.</div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"116 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560207","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