On Perturbations of Generalized Landau-Lifshitz Dynamics

作者：Freidlin Mark^*; Hu Wenqing

来源：Journal of Statistical Physics, 2011, 144(5): 978-1008.

DOI：10.1007/s10955-011-0289-5

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

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.

• 出版日期2011-9