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arXiv · 1608.08194

Homogenization of Dissipative, Noisy, Hamiltonian Dynamics

Jeremiah Birrell·Jan Wehr
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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.

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Jeremiah Birrell, Jan Wehr. 2016-08-29. Homogenization of Dissipative, Noisy, Hamiltonian Dynamics. https://arxiv.org/abs/1608.08194

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