Communications in Mathematical Physics最新文献_第7页

A Gauss–Bonnet Formula for the Renormalized Area of Minimal Submanifolds of Poincaré–Einstein Manifolds 庞加莱-爱因斯坦流形极小子流形重整化面积的Gauss-Bonnet公式

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05228-8

Jeffrey S. Case, C Robin Graham, Tzu-Mo Kuo, Aaron J. Tyrrell, Andrew Waldron

引用次数: 0

Exponential Mixing and Limit Theorems of Quasi-periodically Forced 2D Stochastic Navier–Stokes Equations in the Hypoelliptic Setting 准周期强迫二维随机Navier-Stokes方程的指数混合及极限定理

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05231-7

Rongchang Liu, Kening Lu

{"title":"Exponential Mixing and Limit Theorems of Quasi-periodically Forced 2D Stochastic Navier–Stokes Equations in the Hypoelliptic Setting","authors":"Rongchang Liu, Kening Lu","doi":"10.1007/s00220-025-05231-7","DOIUrl":"10.1007/s00220-025-05231-7","url":null,"abstract":"<div>We consider the incompressible 2D Navier–Stokes equations on the torus driven by a deterministic time quasi-periodic force and a noise that is white in time and degenerate in Fourier space. We show that the asymptotic statistical behavior is characterized by a quasi-periodic invariant measure that exponentially attracts the law of all solutions. The result is true for any value of the viscosity (nu >0) and does not depend on the strength of the external forces. By utilizing this quasi-periodic invariant measure, we establish a quantitative version of the strong law of large numbers and central limit theorem for the continuous time inhomogeneous solution processes with explicit convergence rates. It turns out that the convergence rate in the central limit theorem depends on the time inhomogeneity through the Diophantine approximation property on the quasi-periodic frequency of the quasi-periodic force. The scheme of analyzing the statistical behavior of the time inhomogeneous solution process by the quasi-periodic invariant measure is new and could be extended to other inhomogeneous Markov processes.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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 (varvec{d_gamma /2})-Variation of Distance Profiles in (varvec{gamma })-Liouville Quantum Gravity (varvec{gamma }) -Liouville量子引力中(varvec{d_gamma /2}) -距离分布的变化

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05206-0

Manan Bhatia

{"title":"The (varvec{d_gamma /2})-Variation of Distance Profiles in (varvec{gamma })-Liouville Quantum Gravity","authors":"Manan Bhatia","doi":"10.1007/s00220-024-05206-0","DOIUrl":"10.1007/s00220-024-05206-0","url":null,"abstract":"<div>For Brownian surfaces with boundary and an interior marked point, a natural observable to consider is the distance profile, defined as the process of distances from the marked point to a variable point lying on the boundary. When the boundary is parametrized by the natural length measure on it, this distance profile turns out to be locally absolutely continuous to Brownian motion, and as a result, the boundary length measure itself has a natural interpretation as the quadratic variation process of the distance profile. In this paper, we extend this interpretation to (gamma )-Liouville quantum gravity ((gamma )-LQG), a one-parameter family of models of random geometry which is known to specialize to the case of Brownian geometry for the case (gamma =sqrt{8/3}). With (d_gamma ) denoting the Hausdorff dimension of (gamma )-LQG, we show that for a (gamma )-LQG surface with boundary, the natural boundary length measure can be interpreted (up to a constant factor) as the (d_gamma /2)-variation process of the distance profile from an interior point.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Reflexions on Mahler: Dessins, Modularity and Gauge Theories 对马勒的反思：设计、模块化和规范理论

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-024-05183-4

Jiakang Bao, Yang-Hui He, Ali Zahabi

引用次数: 0

Lower Bound for Simulation Cost of Open Quantum Systems: Lipschitz Continuity Approach 开放量子系统模拟代价的下界：Lipschitz连续性方法

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05240-6

Zhiyan Ding, Marius Junge, Philipp Schleich, Peixue Wu

引用次数: 0

Averaging and Passage Through Resonances in Two-Frequency Systems Near Separatrices 双频系统中近分离的平均共振和通过共振

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05230-8

Anatoly Neishtadt, Alexey Okunev

{"title":"Averaging and Passage Through Resonances in Two-Frequency Systems Near Separatrices","authors":"Anatoly Neishtadt, Alexey Okunev","doi":"10.1007/s00220-025-05230-8","DOIUrl":"10.1007/s00220-025-05230-8","url":null,"abstract":"<div>In this paper we obtain sharp asymptotic estimates for the accuracy of the averaging method for time-periodic perturbations of one-frequency Hamiltonian systems while passing through a separatrix. The Hamiltonian depends on a parameter that slowly changes for the perturbed system (thus, slow–fast Hamiltonian systems with two and a half degrees of freedom are included in our class). Let (varepsilon ) be the small parameter of the system, then under certain genericity conditions we prove that the accuracy of averaging is (O(sqrt{varepsilon }|ln varepsilon |)) for times of order (varepsilon ^{-1}) (such times correspond to a change of slow variables of order 1) for all initial data outside an exceptional set with the measure (O(sqrt{varepsilon }|ln ^5 varepsilon |)). The main novelty of the paper lies in estimating the scattering amplitude and the measure of captured orbits while passing through resonances near separatrices. Our results can also be applied to perturbations of generic two-frequency integrable systems near separatrices, as they can be reduced to periodic perturbations of one-frequency systems.</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Characterization of k-Positive Maps k-正映射的表征

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-17 DOI: 10.1007/s00220-025-05250-4

Tomasz Młynik, Hiroyuki Osaka, Marcin Marciniak

引用次数: 0

On a Variational Problem Related to the Cwikel–Lieb–Rozenblum and Lieb–Thirring Inequalities 关于Cwikel-Lieb-Rozenblum和Lieb-Thirring不等式的一个变分问题

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-07 DOI: 10.1007/s00220-024-05216-y

Thiago Carvalho Corso, Tobias Ried

{"title":"On a Variational Problem Related to the Cwikel–Lieb–Rozenblum and Lieb–Thirring Inequalities","authors":"Thiago Carvalho Corso, Tobias Ried","doi":"10.1007/s00220-024-05216-y","DOIUrl":"10.1007/s00220-024-05216-y","url":null,"abstract":"<div>We explicitly solve a variational problem related to upper bounds on the optimal constants in the Cwikel–Lieb–Rozenblum (CLR) and Lieb–Thirring (LT) inequalities, which has recently been derived in Hundertmark et al. (Invent Math 231:111–167, 2023. https://doi.org/10.1007/s00222-022-01144-7) and Frank et al. (Eur Math Soc 23(8):2583–2600, 2021. https://doi.org/10.1090/pspum/104/01877). We achieve this through a variational characterization of the (L^1) norm of the Fourier transform of a function and duality, from which we obtain a reformulation in terms of a variant of the Hadamard three lines lemma. By studying Hardy-like spaces of holomorphic functions in a strip in the complex plane, we are able to provide an analytic formula for the minimizers, and use it to get the best possible upper bounds for the optimal constants in the CLR and LT inequalities achievable by the method of Hundertmark et al. (Invent Math 231:111–167, 2023. https://doi.org/10.1007/s00222-022-01144-7) and Frank et al. (Eur Math Soc 23(8):2583–2600, 2021. https://doi.org/10.1090/pspum/104/01877).</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05216-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143362060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Crystallization of (hbox {C}^*)-Algebras (hbox {C}^*) -代数的结晶

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-06 DOI: 10.1007/s00220-024-05212-2

Marcelo Laca, Sergey Neshveyev, Makoto Yamashita

{"title":"Crystallization of (hbox {C}^*)-Algebras","authors":"Marcelo Laca, Sergey Neshveyev, Makoto Yamashita","doi":"10.1007/s00220-024-05212-2","DOIUrl":"10.1007/s00220-024-05212-2","url":null,"abstract":"<div>Given a (hbox {C}^*)-algebra A with an almost periodic time evolution (sigma ), we define a new (hbox {C}^*)-algebra (A_c), which we call the crystal of ((A,sigma )), that represents the zero temperature limit of ((A, sigma )). We prove that there is a one-to-one correspondence between the ground states of ((A,sigma )) and the states on (A_c), justifying the name. In order to investigate further the relation between low temperature equilibrium states on A and traces on (A_c), we define a Fock module (mathcal {F}) over the crystal and construct a vacuum representation of A on (mathcal {F}). This allows us to show, under relatively mild assumptions, that for sufficiently large inverse temperatures (beta ) the (sigma )-(hbox {KMS}_beta )-states on A are induced from traces on (A_c) by means of the Fock module. In the second part, we compare the K-theoretic structures of A and (A_c). Previous work by various authors suggests that they have (rationally) isomorphic K-groups. We analyze this phenomenon in detail, confirming it under favorable conditions, but showing that, in general, there is apparently no easy way to relate these groups. As examples, we discuss in particular Exel’s results on semi-saturated circle actions, and recent results of Miller on the K-theory of inverse semigroup (hbox {C}^*)-algebras. In relation to the latter, we introduce the notion of a scale N on an inverse semigroup I and define a new inverse semigroup (I_c), which we call the crystal of (I, N).</div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05212-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

The Tail Distribution of the Partition Function for Directed Polymers in the Weak Disorder Phase 定向聚合物弱无序相配分函数的尾部分布

IF 2.2 1区物理与天体物理

Communications in Mathematical Physics Pub Date : 2025-02-05 DOI: 10.1007/s00220-025-05246-0

Stefan Junk, Hubert Lacoin

引用次数: 0