Homogenization of dissipative, noisy, Hamiltonian dynamics

Jeremiah Birrell, Jan Wehr

Research output: Contribution to journalArticle

4 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2367-2403
Number of pages37
JournalStochastic Processes and their Applications
Volume128
Issue number7
DOIs
StatePublished - Jul 2018

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Keywords

  • Hamiltonian system
  • Homogenization
  • Noise-induced drift
  • Small mass limit

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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