Langevin Equations in the Small-Mass Limit: Higher-Order Approximations

Jeremiah Birrell, Jan Wehr

Research output: Contribution to journalArticle

Abstract

We study the small-mass (overdamped) limit of Langevin equations for a particle in a potential and/or magnetic field with matrix-valued and state-dependent drift and diffusion. We utilize a bootstrapping argument to derive a hierarchy of approximate equations for the position degrees of freedom that are able to achieve accuracy of order m / 2 over compact time intervals for any ℓ∈ Z+. This generalizes prior derivations of the homogenized equation for the position degrees of freedom in the m→ 0 limit, which result in order m1 / 2 approximations. Our results cover bounded forces, for which we prove convergence in Lp norms and unbounded forces, in which case we prove convergence in probability.

Original languageEnglish (US)
Pages (from-to)1765-1811
Number of pages47
JournalAnnales Henri Poincare
Volume21
Issue number6
DOIs
StatePublished - Jun 1 2020

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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