Covariant Formulation of Non-linear Langevin Theory with Multiplicative Gaussian White Noises
Statistical Mechanics
2020-09-16 v2
Abstract
The multi-dimensional non-linear Langevin equation with multiplicative Gaussian white noises in Ito's sense is made covariant with respect to non-linear transform of variables. The formalism involves no metric or affine connection, works for systems with or without detailed balance, and is substantially simpler than previous theories. Its relation with deterministic theory is clarified. The unitary limit and Hermitian limit of the theory are examined. Some implications on the choices of stochastic calculus are also discussed.
Keywords
Cite
@article{arxiv.2007.16131,
title = {Covariant Formulation of Non-linear Langevin Theory with Multiplicative Gaussian White Noises},
author = {Mingnan Ding and Zhanchun Tu and Xiangjun Xing},
journal= {arXiv preprint arXiv:2007.16131},
year = {2020}
}
Comments
12 pages, no figures