The covariant Langevin equation of diffusion on Riemannian manifolds

Fuente: arXiv
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Autor principal: Diósi, Lajos
Formato: Preprint
Publicado: 2023
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author Diósi, Lajos
author_facet Diósi, Lajos
contents 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 equivalent 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.
format Preprint
id arxiv_https___arxiv_org_abs_2310_17314
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The covariant Langevin equation of diffusion on Riemannian manifolds
Diósi, Lajos
Statistical Mechanics
General Relativity and Quantum Cosmology
Mathematical Physics
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 equivalent 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.
title The covariant Langevin equation of diffusion on Riemannian manifolds
topic Statistical Mechanics
General Relativity and Quantum Cosmology
Mathematical Physics
url https://arxiv.org/abs/2310.17314