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Emergence of boundary conditions in the heat equation 热方程中边界条件的出现
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-01 DOI: 10.1063/5.0215656
Jaywan Chung, Seungmin Kang, Ho-Youn Kim, Yong-Jung Kim
{"title":"Emergence of boundary conditions in the heat equation","authors":"Jaywan Chung, Seungmin Kang, Ho-Youn Kim, Yong-Jung Kim","doi":"10.1063/5.0215656","DOIUrl":"https://doi.org/10.1063/5.0215656","url":null,"abstract":"The Dirichlet and Neumann conditions are commonly employed as boundary conditions for the heat equation, yet their legitimacy is debatable in certain scenarios. This paper aims to demonstrate that, in fact, diffusion laws autonomously select boundary conditions. To illustrate this, we incorporate the bounded domain into a larger domain with a diffusivity parameter ϵ > 0 and examine the solution’s behavior at the interface. Our findings reveal that homogeneous Neumann or Dirichlet boundary conditions emerge as ϵ → 0, contingent upon the type of the heterogeneous diffusion.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528543","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
Multiple bound states for a class of fractional critical Schrödinger–Poisson systems with critical frequency 一类具有临界频率的分数临界薛定谔-泊松系统的多重约束状态
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-07-01 DOI: 10.1063/5.0174872
Xiaoming He, Yuxi Meng, Patrick Winkert
{"title":"Multiple bound states for a class of fractional critical Schrödinger–Poisson systems with critical frequency","authors":"Xiaoming He, Yuxi Meng, Patrick Winkert","doi":"10.1063/5.0174872","DOIUrl":"https://doi.org/10.1063/5.0174872","url":null,"abstract":"In this paper we study the fractional Schrödinger–Poisson system ε2s(−Δ)su+V(x)u=ϕ|u|2s*−3u+|u|2s*−2u,ε2s(−Δ)sϕ=|u|2s*−1,x∈R3, where s ∈ (0, 1), ɛ > 0 is a small parameter, 2s*=63−2s is the critical Sobolev exponent and V∈L32s(R3) is a nonnegative function which may be zero in some regions of R3, e.g., it is of the critical frequency case. By virtue of a new global compactness lemma, and the Lusternik–Schnirelmann category theory, we relate the number of bound state solutions with the topology of the zero set where V attains its minimum for small values of ɛ.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141528541","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
Topological spectral bands with frieze groups 带有楣群的拓扑谱带
IF 1.3 3区 物理与天体物理
Journal of Mathematical Physics Pub Date : 2024-06-28 DOI: 10.1063/5.0127973
Fabian R. Lux, Tom Stoiber, Shaoyun Wang, Guoliang Huang, Emil Prodan
{"title":"Topological spectral bands with frieze groups","authors":"Fabian R. Lux, Tom Stoiber, Shaoyun Wang, Guoliang Huang, Emil Prodan","doi":"10.1063/5.0127973","DOIUrl":"https://doi.org/10.1063/5.0127973","url":null,"abstract":"Frieze groups are discrete subgroups of the full group of isometries of a flat strip. We investigate here the dynamics of specific architected materials generated by acting with a frieze group on a collection of self-coupling seed resonators. We demonstrate that, under unrestricted reconfigurations of the internal structures of the seed resonators, the dynamical matrices of the materials generate the full self-adjoint sector of the stabilized group C*-algebra of the frieze group. As a consequence, in applications where the positions, orientations and internal structures of the seed resonators are adiabatically modified, the spectral bands of the dynamical matrices carry a complete set of topological invariants that are fully accounted by the K-theory of the mentioned algebra. By resolving the generators of the K-theory, we produce the model dynamical matrices that carry the elementary topological charges, which we implement with systems of plate resonators to showcase several applications in spectral engineering. The paper is written in an expository style.","PeriodicalId":16174,"journal":{"name":"Journal of Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509064","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
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
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