Homogenization of Dissipative, Noisy, Hamiltonian Dynamics

TL;DR

This paper derives a homogenized equation for dissipative, noisy Hamiltonian systems in the small mass limit, revealing a noise-induced drift and proving convergence with applications in physics.

Contribution

It introduces a rigorous derivation of the homogenized dynamics including noise effects and noise-induced drift in dissipative Hamiltonian systems.

Findings

Derived the homogenized equation with noise-induced drift

Proved convergence in probability and in $L^p$-norm

Applied results to particle motion and nuclear matter dynamics

Abstract

We study the dynamics of a class of Hamiltonian systems with dissipation, coupled to noise, in a singular (small mass) limit. We derive the homogenized equation for the position degrees of freedom in the limit, including the presence of a {\em noise-induced drift} term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an $L^p$-norm. Applications cover the overdamped limit of particle motion in a time-dependent electromagnetic field, on a manifold with time-dependent metric, and the dynamics of nuclear matter.