arXiv: Mathematical Physics最新文献_第5页

Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media 无序介质中自由费米子微观电流的量子涨落和大偏差原理

arXiv: Mathematical Physics Pub Date : 2020-07-25 DOI: 10.2140/PAA.2020.2.205

J. Bru, W. Pedra, A. Ratsimanetrimanana

{"title":"Quantum Fluctuations and Large Deviation Principle for Microscopic Currents of Free Fermions in Disordered Media","authors":"J. Bru, W. Pedra, A. Ratsimanetrimanana","doi":"10.2140/PAA.2020.2.205","DOIUrl":"https://doi.org/10.2140/PAA.2020.2.205","url":null,"abstract":"We contribute an extension of large-deviation results obtained in [N.J.B. Aza, J.-B. Bru, W. de Siqueira Pedra, A. Ratsimanetrimanana, J. Math. Pures Appl. 125 (2019) 209] on conductivity theory at atomic scale of free lattice fermions in disordered media. Disorder is modeled by (i) a random external potential, like in the celebrated Anderson model, and (ii) a nearest-neighbor hopping term with random complex-valued amplitudes. In accordance with experimental observations, via the large deviation formalism, our previous paper showed in this case that quantum uncertainty of microscopic electric current densities around their (classical) macroscopic value is suppressed, exponentially fast with respect to the volume of the region of the lattice where an external electric field is applied. Here, the quantum fluctuations of linear response currents are shown to exist in the thermodynamic limit and we mathematically prove that they are related to the rate function of the large deviation principle associated with current densities. We also demonstrate that, in general, they do not vanish (in the thermodynamic limit) and the quantum uncertainty around the macroscopic current density disappears exponentially fast with an exponential rate proportional to the squared deviation of the current from its macroscopic value and the inverse current fluctuation, with respect to growing space (volume) scales.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75087250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A note on generalized fractional diffusion equations on Poincaré half plane 关于庞卡罗半平面上广义分数扩散方程的一个注记

arXiv: Mathematical Physics Pub Date : 2020-07-23 DOI: 10.7153/fdc-2021-11-07

R. Garra, F. Maltese, E. Orsingher

引用次数: 2

Product Matrix Processes With Symplectic and Orthogonal Invariance via Symmetric Functions 具有辛不变性和正交不变性的对称函数积矩阵过程

arXiv: Mathematical Physics Pub Date : 2020-07-23 DOI: 10.1093/IMRN/RNAB045

Andrew Ahn, E. Strahov

引用次数: 4

Quadratic first integrals of autonomous conservative dynamical systems 自主保守动力系统的二次第一积分

arXiv: Mathematical Physics Pub Date : 2020-07-21 DOI: 10.1063/1.5141392

M. Tsamparlis, Antonios Mitsopoulos

{"title":"Quadratic first integrals of autonomous conservative dynamical systems","authors":"M. Tsamparlis, Antonios Mitsopoulos","doi":"10.1063/1.5141392","DOIUrl":"https://doi.org/10.1063/1.5141392","url":null,"abstract":"An autonomous dynamical system is described by a system of second order differential equations whose solution gives the trajectories of the system. The solution is facilitated by the use of first integrals (FIs) that are used to reduce the order of the system of differential equations and, if there are enough of them, to determine the solution. Therefore, it is important that there exists a systematic method to determine the FIs. On the other hand, a system of second order differential equations defines a kinetic energy, which provides a symmetric second order tensor called kinetic metric of the system. This metric via its symmetries brings into the scene the numerous methods of differential geometry and hence it is apparent that one should manage to relate the determination of the FIs to the symmetries of the kinetic metric. The subject of this work is to provide a theorem that realizes this scenario. The method we follow considers the generic quadratic FI of the form $I=K_{ab}(t,q^{c})dot{q}^{a}dot{q}^{b}+K_{a}(t,q^{c})dot{q}^{a} +K(t,q^{c})$ where $K_{ab}(t,q^{c}), K_{a}(t,q^{c}), K(t,q^{c})$ are unknown tensor quantities and requires $dI/dt = 0$. This condition leads to a system of differential equations involving the coefficients of $I$ whose solution provides all possible quadratic FIs of this form. We demonstrate the application of the theorem in the classical cases of the geodesic equations and the generalized Kepler potential. We also obtain and discuss the time-dependent FIs.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82993655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

On the bi-Hamiltonian Structure of the Trigonometric Spin Ruijsenaars–Sutherland Hierarchy 三角自旋rujsenaars - sutherland层次的双哈密顿结构

arXiv: Mathematical Physics Pub Date : 2020-07-19 DOI: 10.1007/978-3-030-53305-2_5

L. Fehér, I. Marshall

引用次数: 0

Nonlocal symmetry of CMA generates ASD Ricci-flat metric with no Killing vectors CMA的非局部对称性产生无杀伤向量的ASD ricci平面度量

arXiv: Mathematical Physics Pub Date : 2020-07-16 DOI: 10.1063/5.0022021

M. Sheftel

引用次数: 1

Scattering theory for a class of non-selfadjoint extensions of symmetric operators 一类非自伴随对称算子扩展的散射理论

arXiv: Mathematical Physics Pub Date : 2020-07-15 DOI: 10.1007/978-3-030-31531-3_14

K. Cherednichenko, A. Kiselev, Luis O. Silva