黎曼曼体上扩散的共变朗格文方程

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-10-01 DOI:10.1016/S0034-4877(24)00073-9

Lajos Diósi

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引用次数: 0

摘要

多变量扩散漂移过程的协变形式由协变福克-普朗克方程利用黎曼几何的标准工具箱来描述。物理学和数学界长期以来一直在寻求改编朗之文随机微分方程的协变形式。我们的研究表明，最简单的协变斯特拉托诺维奇随机微分方程取决于局部正交框架（参见 vielbein），只要我们施加额外的协变约束：框架的矢量必须是无发散的，它就会变成所需的协变朗格文方程。

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The Covariant Langevin Equation of Diffusion on Riemannian Manifolds

The covariant form of the multivariable diffusion-drift process is described by the covariant Fokker–Planck equation using the standard toolbox of Riemann geometry. The covariant form of the adapted Langevin stochastic differential equation is long sought after in both physics and mathematics. We show that the simplest covariant Stratonovich stochastic differential equation depending on the local orthogonal frame (cf. vielbein) becomes the desired covariant Langevin equation provided we impose an additional covariant constraint: the vectors of the frame must be divergence-free.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.