Homogenization of dissipative, noisy, Hamiltonian dynamics

Jeremiah Birrell and Jan Wehr

Stochastic Processes and their Applications, 2018, vol. 128, issue 7, 2367-2403

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 noise-induced drift term. We prove convergence to the solution of the homogenized equation in probability and, under stronger assumptions, in an Lp-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.

Keywords: Hamiltonian system; Homogenization; Small mass limit; Noise-induced drift (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2017.09.005

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