On Perturbations of Generalized Landau-Lifshitz Dynamics

Mark Freidlin, Wenqing Hu

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Abstract

We consider deterministic and stochastic perturbations of dynamical systems with conservation laws in ℝ 3. The Landau-Lifshitz equation for the magnetization dynamics in ferromagnetics is a special case of our system. The averaging principle is a natural tool in such problems. But bifurcations in the set of invariant measures lead to essential modification in classical averaging. The limiting slow motion in this case, in general, is a stochastic process even if pure deterministic perturbations of a deterministic system are considered. The stochasticity is a result of instabilities in the non-perturbed system as well as of existence of ergodic sets of a positive measure. We effectively describe the limiting slow motion.

Original languageEnglish (US)
Pages (from-to)978-1008
Number of pages31
JournalJournal of Statistical Physics
Volume144
Issue number5
DOIs
StatePublished - Sep 2011

Bibliographical note

Funding Information:
This work is supported in part by NSF Grants DMS-0803287 and DMS-0854982.

Keywords

  • Averaging principle
  • Landau-Lifshitz equation
  • Magnetization dynamics
  • Stochasticity in deterministic systems

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