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Existence of periodic measures of fractional stochastic delay complex Ginzburg-Landau equations on Rn Rn 上分数随机延迟复合金兹堡-朗道方程的周期量的存在性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-06-27 DOI: 10.1063/5.0180975
Zhiyu Li, Xiaomin Song, Gang He, Ji Shu
{"title":"Existence of periodic measures of fractional stochastic delay complex Ginzburg-Landau equations on Rn","authors":"Zhiyu Li, Xiaomin Song, Gang He, Ji Shu","doi":"10.1063/5.0180975","DOIUrl":"https://doi.org/10.1063/5.0180975","url":null,"abstract":"This paper is concerned with periodic measures of fractional stochastic complex Ginzburg–Landau equations with variable time delay on unbounded domains. We first derive the uniform estimates of solutions. Then we establish the regularity and prove the equicontinuity of solutions in probability, which is used to prove the tightness of distributions of solutions. In order to overcome the non-compactness of Sobolev embeddings on unbounded domains, we use the uniform estimates on the tails in probability. As a result, we prove the existence of periodic measures by combining Arzelà-Ascoli theorem and Krylov-Bogolyubov method.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528544","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
Mixed state representability of entropy-density pairs 熵密度对的混合状态可表示性
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-06-26 DOI: 10.1063/5.0169120
Louis Garrigue
{"title":"Mixed state representability of entropy-density pairs","authors":"Louis Garrigue","doi":"10.1063/5.0169120","DOIUrl":"https://doi.org/10.1063/5.0169120","url":null,"abstract":"We show the representability of density-entropy pairs with canonical and grand-canonical states, and we provide bounds on the kinetic energy of the representing states.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509065","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
Necessary and sufficient conditions of entire sub-solutions for a (k1, k2)-type Hessian systems with gradient terms 带梯度项的（k1, k2）型 Hessian 系统全子解的必要条件和充分条件
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-06-24 DOI: 10.1063/5.0192926
Chenghua Gao, Xingyue He
{"title":"Necessary and sufficient conditions of entire sub-solutions for a (k1, k2)-type Hessian systems with gradient terms","authors":"Chenghua Gao, Xingyue He","doi":"10.1063/5.0192926","DOIUrl":"https://doi.org/10.1063/5.0192926","url":null,"abstract":"In this paper, we aim to discuss a class of (k1, k2)-type Hessian system with gradient terms. In the case of k1 = k2 = 1 and 2 ≤ k1, k2 ≤ n, we obtain a sufficient and necessary condition for the existence of the entire admissible sub-solution of the system according to the value range of different parameters, which is also called the generalized Keller–Osserman condition. Based on this, we also discuss the conditions of existence and non-existence of the entire sub-solution, respectively. Finally, we extend the nonlinear terms to the degenerate case and consider the condition of the existence of the positive sub-solution for the above system.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509066","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
Symplectic and Lagrangian polar duality; applications to quantum harmonic analysis 交映和拉格朗日极性对偶；量子谐波分析的应用
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-06-21 DOI: 10.1063/5.0192334
Maurice de Gosson, Charlyne de Gosson
{"title":"Symplectic and Lagrangian polar duality; applications to quantum harmonic analysis","authors":"Maurice de Gosson, Charlyne de Gosson","doi":"10.1063/5.0192334","DOIUrl":"https://doi.org/10.1063/5.0192334","url":null,"abstract":"Polar duality is a well-known concept from convex geometry and analysis. In the present paper we study a symplectically covariant versions of polar duality, having in mind their applications to quantum harmonic analysis. It makes use of the standard symplectic form on phase space and allows a precise study of the covariance matrix of a density operator.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528546","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
Precise asymptotics for the spectral radius of a large random matrix 大型随机矩阵谱半径的精确渐近线
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-06-21 DOI: 10.1063/5.0209705
Giorgio Cipolloni, László Erdős, Yuanyuan Xu
{"title":"Precise asymptotics for the spectral radius of a large random matrix","authors":"Giorgio Cipolloni, László Erdős, Yuanyuan Xu","doi":"10.1063/5.0209705","DOIUrl":"https://doi.org/10.1063/5.0209705","url":null,"abstract":"We consider the spectral radius of a large random matrix X with independent, identically distributed entries. We show that its typical size is given by a precise three-term asymptotics with an optimal error term beyond the radius of the celebrated circular law. The coefficients in this asymptotics are universal but they differ from a similar asymptotics recently proved for the rightmost eigenvalue of X in Cipolloni et al., Ann. Probab. 51(6), 2192–2242 (2023). To access the more complicated spectral radius, we need to establish a new decorrelation mechanism for the low-lying singular values of X − z for different complex shift parameters z using the Dyson Brownian Motion.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528545","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
Properties of weak solutions to the Nordström–Vlasov system 诺德斯特伦-弗拉索夫系统弱解的性质
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-06-20 DOI: 10.1063/5.0150177
Meixia Xiao
{"title":"Properties of weak solutions to the Nordström–Vlasov system","authors":"Meixia Xiao","doi":"10.1063/5.0150177","DOIUrl":"https://doi.org/10.1063/5.0150177","url":null,"abstract":"In this article, we investigate the Nordström–Vlasov system in the whole space. The kinetic model is a relativistic generalization of the classical Vlasov–Poisson system in the gravitational case and describes the ensemble motion of collisionless particles interacting by means of a self-consistent scalar gravitational field. With the Fourier analysis and the smoothing effect of low velocity particles, we get a better regularity of weak solutions for the field than the one proved by Calogero and Rein [J. Differ. Equ. 204, 323 (2004)]. Meanwhile, under the additional integrability condition, we establish the energy conservation of the weak solution.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528547","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
Homotopy of periodic 2 × 2 matrices 周期性 2 × 2 矩阵的同调
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-05-30 DOI: 10.1063/5.0138809
Joseph E. Avron, Ari M. Turner
{"title":"Homotopy of periodic 2 × 2 matrices","authors":"Joseph E. Avron, Ari M. Turner","doi":"10.1063/5.0138809","DOIUrl":"https://doi.org/10.1063/5.0138809","url":null,"abstract":"We describe the homotopy classes of loops in the space of 2 × 2 simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in R3/{0}. Since closed curves in R3/{0} can be readily visualized, no advanced tools of algebraic topology are needed. The matrices represent gapped Bloch Hamiltonians in 1D with a two dimensional Hilbert space per unit cell.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141198334","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
Point particle E-models 点粒子 E 模型
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-05-24 DOI: 10.1063/5.0159748
Ctirad Klimčík
{"title":"Point particle E-models","authors":"Ctirad Klimčík","doi":"10.1063/5.0159748","DOIUrl":"https://doi.org/10.1063/5.0159748","url":null,"abstract":"We show that the same algebraic data that permit to construct the Lax pair and the r-matrix of an integrable non-linear σ-model in 1 + 1 dimensions can be also used for the construction of Lax pairs and of r-matrices of several other non-trivial integrable theories in 1 + 0 dimension. We call those new integrable theories the point particle E-models, we describe their structure and give their physical interpretation. We work out in detail the point particle E-modelsassociated to the bi-Yang–Baxter deformation of the SU(N) principal chiral model. In particular, for each complex flag manifold we thus obtain a two-parameter family of integrable models living on it.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152566","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
Optimal semiclassical regularity of projection operators and strong Weyl law 投影算子的最优半经典正则性和强韦尔定律
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-05-23 DOI: 10.1063/5.0191089
Laurent Lafleche
{"title":"Optimal semiclassical regularity of projection operators and strong Weyl law","authors":"Laurent Lafleche","doi":"10.1063/5.0191089","DOIUrl":"https://doi.org/10.1063/5.0191089","url":null,"abstract":"Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of quantum mechanics, projection operators can be seen as the analogue of characteristic functions of subsets of the phase space, which are discontinuous functions. We prove that projection operators indeed converge to characteristic functions of the phase space and that in terms of quantum Sobolev spaces, they exhibit the same maximal regularity as characteristic functions. This can be interpreted as a semiclassical asymptotic on the size of commutators in Schatten norms. Our study answers a question raised in Chong et al. [J. Eur. Math. Soc. (unpublished) (2024)] about the possibility of having projection operators as initial data. It also gives a strong convergence result in Sobolev spaces for the Weyl law in phase space.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152584","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
Two types of Witten zeta functions 两类维滕 zeta 函数
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-05-16 DOI: 10.1063/5.0188248
A. Levin, M. Olshanetsky
{"title":"Two types of Witten zeta functions","authors":"A. Levin, M. Olshanetsky","doi":"10.1063/5.0188248","DOIUrl":"https://doi.org/10.1063/5.0188248","url":null,"abstract":"We define two types of Witten’s zeta functions according to Cartan’s classification of compact symmetric spaces. The type II is the original Witten zeta function constructed by means of irreducible representations of the simple compact Lie group U. The type I Witten zeta functions, we introduce here, are related to the irreducible spherical representations of U. They arise in the harmonic analysis on compact symmetric spaces of the form U/K, where K is the maximal subgroup of U. To construct the type I zeta function we calculate the partition functions of 2d YM theory with broken gauge symmetry using the Migdal–Witten approach. We prove that for the rank one symmetric spaces the generating series for the values of the type I functions with integer arguments can be defined in terms of the generating series of the Riemann zeta-function.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063182","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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