Mathematical Physics, Analysis and Geometry最新文献_第3页

A phase space localization operator in negative binomial states 负二项状态下的相空间定位算子

IF 1.1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-07-10 DOI: 10.1007/s11040-025-09512-4

Zouhaïr Mouayn, Soumia Touhami, Samah Aslaoui

{"title":"A phase space localization operator in negative binomial states","authors":"Zouhaïr Mouayn, Soumia Touhami, Samah Aslaoui","doi":"10.1007/s11040-025-09512-4","DOIUrl":"10.1007/s11040-025-09512-4","url":null,"abstract":"<div>We study the spectral properties of the phase space localization operator (P_{R}), defined by the indicator function of a disk (D_{R}) of radius (R<1.) The localization is performed using a family of negative binomial states (NBS), labeled by points z in the unit disk (mathbb {D}) and parameterized by (nu > {frac{1}{2}}). These states are intrinsically connected to the 1D pseudo-harmonic oscillator (PHO) through superpositions of its eigenfunctions. The superposition coefficients form an orthonormal basis of a weighted Bergman space (mathcal {A}^{nu }left( mathbb {D}right) ), which also emerges as the eigenspace of a 2D Schrödinger operator with a magnetic field (proportional to (nu )) corresponding to the lowest hyperbolic Landau level. The eigenvalues (lambda _{j}^{nu ,R}) of (P_{R}) were obtained via a discrete spectral resolution within a shared eigenbasis for (P_{R}) and the PHO. By using these eigenvalues we obtain a closed-form expression for the variance of the particle count in (D_{R}) under the determinantal point process (DPP) defined by the weighted Bergman kernel. Beyond (D_{R}), the phase space content of (P_{R}) was estimated via the NBS photon-counting distribution, revealing a non-zero residual contribution. Using the coherent state transform associated with NBS, we mapped (P_{R}) to (mathcal {A}^{nu }left( mathbb {D}right) ) and we derive its explicit integral kernel (K_{nu ,R}left( z,wright) ), which converges to the Bergman kernel (K_{nu }left( z,wright) ) as (Rrightarrow 1).</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 3","pages":""},"PeriodicalIF":1.1,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164251","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

Variation behind Modular Gaussian Curvature and Cyclic Structure 模高斯曲率和循环结构背后的变化

IF 1.1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-07-04 DOI: 10.1007/s11040-025-09510-6

Yang Liu

引用次数: 0

Analysis for idempotent states on quantum permutation groups 量子置换群上幂等态的分析

IF 1.1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-07-02 DOI: 10.1007/s11040-025-09511-5

J. P. McCarthy

引用次数: 0

Topological indices for periodic gapped Hamiltonians and fuzzy tori 周期间隙哈密顿算子和模糊环面的拓扑指标

IF 1.1 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-06-13 DOI: 10.1007/s11040-025-09508-0

Nora Doll, Terry Loring, Hermann Schulz-Baldes

引用次数: 0

Essential Self-Adjointness of the Laplacian on Weighted Graphs: Harmonic Functions, Stability, Characterizations and Capacity 加权图上拉普拉斯算子的本质自伴随性：调和函数、稳定性、刻画和容量

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-26 DOI: 10.1007/s11040-025-09498-z

Atsushi Inoue, Sean Ku, Jun Masamune, Radosław K. Wojciechowski

引用次数: 0

The Ricci Curvature and the Normalized Ricci Flow on Generalized Wallach Spaces 广义Wallach空间上的Ricci曲率和归一化Ricci流

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-20 DOI: 10.1007/s11040-025-09509-z

Nurlan A. Abiev

{"title":"The Ricci Curvature and the Normalized Ricci Flow on Generalized Wallach Spaces","authors":"Nurlan A. Abiev","doi":"10.1007/s11040-025-09509-z","DOIUrl":"10.1007/s11040-025-09509-z","url":null,"abstract":"<div>We proved that the normalized Ricci flow does not preserve the positivity of the Ricci curvature of invariant Riemannian metrics on every generalized Wallach space with (a_1+a_2+a_3le 1/2), in particular, such a property takes place on the homogeneous spaces (operatorname {SU}(k+l+m)/operatorname {S}(operatorname {U}(k)times operatorname {U}(l) times operatorname {U}(m))) and (operatorname {Sp}(k+l+m)/operatorname {Sp}(k)times operatorname {Sp}(l) times operatorname {Sp}(m)) independently on their parameters k, l and m. We proved that the positivity of the Ricci curvature is preserved under the normalized Ricci flow on generalized Wallach spaces with (a_1+a_2+a_3> 1/2) if the conditions (4left( a_j+a_kright) ^2ge (1-2a_i)(1+2a_i)^{-1}) are satisfied for all ({i,j,k}={1,2,3}). We also established that the homogeneous spaces (operatorname {SO}(k+l+m)/operatorname {SO}(k)times operatorname {SO}(l)times operatorname {SO}(m)) satisfy the above conditions if (max {k,l,m}le 11), moreover, additional conditions were found to keep (operatorname {Ric}>0) in cases when (max {k,l,m}le 11) is violated. Answers have also been found to similar questions about maintaining or non-maintaining the positivity of the Ricci curvature on all other generalized Wallach spaces given in the classification of Yu. G. Nikonorov.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144090984","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

Analysis of Gibbs Measures and Stability of Dynamical System Linked to (1,1/2)-Mixed Ising Model on ((m,k))-Ary Trees ((m,k)) -Ary树上(1,1/2)-混合Ising模型动力学系统的Gibbs测度及稳定性分析

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-04 DOI: 10.1007/s11040-025-09504-4

Aminah Qawasmeh, Farrukh Mukhamedov, Hasan Akın

{"title":"Analysis of Gibbs Measures and Stability of Dynamical System Linked to (1,1/2)-Mixed Ising Model on ((m,k))-Ary Trees","authors":"Aminah Qawasmeh, Farrukh Mukhamedov, Hasan Akın","doi":"10.1007/s11040-025-09504-4","DOIUrl":"10.1007/s11040-025-09504-4","url":null,"abstract":"<div>This paper introduces a new (1,1/2) mixed spin Ising model (shortly, (1,1/2)-MSIM) having (J_1) and (J_2) competing interactions on (m, k)-ary trees. By constructing splitting Gibbs measures, we establish the presence of multiple Gibbs measures, which implies the occurrence of the phase transition for the (1, 1/2)-MSIM on the (m, k)-ary trees. Furthermore, the extremality of the two translation-invariant Gibbs measures is demonstrated for (1, k)-ary trees. Moreover, the extremality condition for the disordered phases is found and its non-extremality regimes are examined as well. It is well known that, to investigate lattice models on tree-like structures, conducting a stability analysis of the dynamical systems that represent the model and examining the behavior of the fixed points of these dynamical systems can provide significant insights into the model. We conducted a stability analysis around fixed points to investigate the behavior of the MSIM on the (m, k)-ary trees, also referred to as k-ary trees.</div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2025-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904792","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

Gauge Transformations and Long-Time Asymptotics for the New Coupled Integrable Dispersionless Equations 新耦合可积无色散方程的规范变换和长渐近性

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-05-02 DOI: 10.1007/s11040-025-09507-1

Xumeng Zhou, Xianguo Geng, Minxin Jia, Yunyun Zhai

引用次数: 0

Classification of (1+0) Two-Dimensional Hamiltonian Operators (1+0)二维哈密顿算子的分类

IF 0.9 3区数学

Mathematical Physics, Analysis and Geometry Pub Date : 2025-04-29 DOI: 10.1007/s11040-025-09506-2

Alessandra Rizzo

引用次数: 0

Notions of Fermionic Entropies for Causal Fermion Systems 因果费米子系统的费米子熵概念