Analytical Description of Quasi-Random Magnetization Relaxation to Equilibrium

The Landau-Lifshitz (LL) dynamics of a uniformly magnetized particle is considered. The LL equation is written in the form of a Hamiltonian perturbed dynamical system. By using suitable averaging technique, the equation for the slow dynamics of the energy is derived. The averaging technique breaks up in the case of separatrix crossing. It is shown that, in the limit of small damping, the separatrix crossing can be described by using a probabilistic approach.