Annales Henri Poincaré最新文献_第8页

Random Covariant Quantum Channels 随机协变量子信道

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-26 DOI: 10.1007/s00023-025-01558-y

Ion Nechita, Sang-Jun Park

引用次数: 0

Mean Eigenvector Self-Overlap in the Real and Complex Elliptic Ginibre Ensembles at Strong and Weak Non-Hermiticity 强、弱非密性下实数和复椭圆Ginibre系综的平均特征向量自重叠

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-21 DOI: 10.1007/s00023-024-01530-2

Mark J. Crumpton, Yan V. Fyodorov, Tim R. Würfel

{"title":"Mean Eigenvector Self-Overlap in the Real and Complex Elliptic Ginibre Ensembles at Strong and Weak Non-Hermiticity","authors":"Mark J. Crumpton, Yan V. Fyodorov, Tim R. Würfel","doi":"10.1007/s00023-024-01530-2","DOIUrl":"10.1007/s00023-024-01530-2","url":null,"abstract":"<div><p>We study the mean diagonal overlap of left and right eigenvectors associated with complex eigenvalues in <span>(Ntimes N)</span> non-Hermitian random Gaussian matrices. In a well-known work by Chalker and Mehlig the expectation of this (self-)overlap was computed for the complex Ginibre ensemble as <span>(Nrightarrow infty )</span> (Chalker and Mehlig in Phys Rev Lett 81(16):3367–3370, 1998). In the present work, we consider the same quantity in the real and complex elliptic Ginibre ensembles, which are characterised by correlations between off-diagonal entries controlled by a parameter <span>(tau in [0,1])</span>, with <span>(tau =1)</span> corresponding to the Hermitian limit. We derive exact expressions for the mean diagonal overlap in both ensembles at any finite <i>N</i>, for any eigenvalue off the real axis. We further investigate several scaling regimes as <span>(Nrightarrow infty )</span>, both in the limit of strong non-Hermiticity keeping a fixed <span>(tau in [0,1))</span> and in the weak non-Hermiticity limit, with <span>(tau )</span> approaching unity in such a way that <span>(N(1-tau ))</span> remains finite.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 6","pages":"2069 - 2116"},"PeriodicalIF":1.3,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01530-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167319","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 Diffusion Approximation of the Stationary Radiative Transfer Equation with Absorption and Emission 带吸收和发射的平稳辐射传递方程的扩散近似

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-18 DOI: 10.1007/s00023-025-01556-0

Elena Demattè, Juan J. L. Velázquez

{"title":"On the Diffusion Approximation of the Stationary Radiative Transfer Equation with Absorption and Emission","authors":"Elena Demattè, Juan J. L. Velázquez","doi":"10.1007/s00023-025-01556-0","DOIUrl":"10.1007/s00023-025-01556-0","url":null,"abstract":"<div><p>In this paper, we study the distribution of temperature of a body due to the transfer of radiation. Specifically, the boundary value problem for the stationary radiative transfer equation is considered. In all the analysis, we assume the so-called local thermal equilibrium (LTE), i.e., there is a well-defined temperature of the body at each point. We consider the limit in which the mean free path of the photons is much smaller than the characteristic length of the domain. In this case, we can approximate the solution by means of the so-called diffusion approximation. The analysis of this paper is restricted to the case in which the absorption coefficient is independent of the frequency <span>( nu )</span> (the so-called Grey approximation). We ignore also scattering effects. Under these assumptions, we show that the density of radiative energy <i>u</i>, which is proportional to the fourth power of the temperature, solves in the limit an elliptic equation. The boundary values for that limit equation can be determined uniquely analyzing a suitable boundary layer problem. The method developed here allows to prove all the results using maximum principle arguments for a class of non-local elliptic equations.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 3","pages":"1075 - 1163"},"PeriodicalIF":1.3,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01556-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441472","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

Local Time Decay for Fractional Schrödinger Operators with Slowly Decaying Potentials 具有慢衰减势的分数阶Schrödinger算子的局部时间衰减

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-17 DOI: 10.1007/s00023-025-01560-4

Kouichi Taira

引用次数: 0

Examples of Small-Time Controllable Schrödinger Equations 小时间可控Schrödinger方程的例子

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-15 DOI: 10.1007/s00023-025-01559-x

Karine Beauchard, Eugenio Pozzoli

引用次数: 0

Quenched Large Deviations of Birkhoff Sums Along Random Quantum Measurements 随随机量子测量的Birkhoff和的淬灭大偏差

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-12 DOI: 10.1007/s00023-025-01553-3

R. Raquépas, J. Schenker

引用次数: 0

Order p Quantum Wasserstein Distances from Couplings p阶量子瓦瑟斯坦距离

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-11 DOI: 10.1007/s00023-025-01557-z

Emily Beatty, Daniel Stilck França

{"title":"Order p Quantum Wasserstein Distances from Couplings","authors":"Emily Beatty, Daniel Stilck França","doi":"10.1007/s00023-025-01557-z","DOIUrl":"10.1007/s00023-025-01557-z","url":null,"abstract":"<div><p>Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the <i>p</i>-Wasserstein distance, which serves to quantify the cost of transporting one probability measure to another. While recent attempts have sought to extend this measure to the realm of quantum states, existing definitions often present certain limitations, such as not being faithful. In this work, we present a new definition of quantum Wasserstein distances. This definition, leveraging the coupling method and a metric applicable to pure states, draws inspiration from a property characterising the classical Wasserstein distance—its determination based on its value on point masses. Subject to certain continuity properties, our definition exhibits numerous attributes expected of an optimal quantum rendition of the Wasserstein distance. Notably, our approach seamlessly integrates metrics familiar to quantum information theory, such as the trace distance. Moreover, it provides an organic extension for metrics, like Nielsen’s complexity metric, allowing their application to mixed states with a natural operational interpretation. We analyse this metric’s attributes in the context of random quantum states, unveil phase transitions concerning the complexity of subsystems of random states and use it to derive circuit lower bounds. In addition, we show how we can use our definition to study hypercontractive inequalities for quantum channels that do not admit a faithful fixed point, allowing us to derive concentration inequalities. Finally, we discuss how our distance is well suited to define quantum Wasserstein generative adversarial networks.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 3","pages":"787 - 845"},"PeriodicalIF":1.3,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441163","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

Horseshoes for a Class of Nonuniformly Expanding Random Circle Maps 一类非均匀展开随机圆映射的马蹄铁

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-05 DOI: 10.1007/s00023-025-01555-1

Jeroen S. W. Lamb, Giuseppe Tenaglia, Dmitry Turaev

引用次数: 0

Hamiltonian Formulation and Aspects of Integrability of Generalised Hydrodynamics 广义流体力学的哈密顿公式和可积性

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-03-03 DOI: 10.1007/s00023-025-01546-2

Thibault Bonnemain, Vincent Caudrelier, Benjamin Doyon

{"title":"Hamiltonian Formulation and Aspects of Integrability of Generalised Hydrodynamics","authors":"Thibault Bonnemain, Vincent Caudrelier, Benjamin Doyon","doi":"10.1007/s00023-025-01546-2","DOIUrl":"10.1007/s00023-025-01546-2","url":null,"abstract":"<div><p>Generalised hydrodynamics (GHD) describes the large-scale inhomogeneous dynamics of integrable (or close to integrable) systems in one dimension of space, based on a central equation for the fluid density or quasi-particle density: the GHD equation. We consider a new, general form of the GHD equation: we allow for spatially extended interaction kernels, generalising previous constructions. We show that the GHD equation, in our general form and hence also in its conventional form, is Hamiltonian. This holds also including force terms representing inhomogeneous external potentials coupled to conserved densities. To this end, we introduce a new Poisson bracket on functionals of the fluid density, which is seen as our dynamical field variable. The total energy is the Hamiltonian whose flow under this Poisson bracket generates the GHD equation. The fluid density depends on two (real and spectral) variables, and the GHD equation can be seen as a <span>(2+1)</span>-dimensional classical field theory. In its <span>(1+1)</span>-dimensional reduction corresponding to the case without external forces, we further show the system admits an infinite set of conserved quantities that are in involution for our Poisson bracket, hinting at integrability of this field theory.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"27 1","pages":"287 - 345"},"PeriodicalIF":1.3,"publicationDate":"2025-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-025-01546-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145948096","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

Ergodic and Non-Ergodic Phenomena in One-Dimensional Random Processes: Exploring Unconventional State Transitions 一维随机过程中的遍历与非遍历现象：探索非常规状态转换

IF 1.3 3区物理与天体物理

Annales Henri Poincaré Pub Date : 2025-02-28 DOI: 10.1007/s00023-025-01554-2

A. D. Ramos, C. S. Sousa, L. P. Cavalcanti

引用次数: 0