Eur. Phys. J. B 69, 445-454 (2009)
https://doi.org/10.1140/epjb/e2009-00167-6

Dynamics of spinor condensates and stochastic approach

¹ Department of Physics, Ritsumeikan University-BKC, Noji-Hill, Kusatsu City, 525-8577, Japan
² Laboratoire de Physique des Solides Bât. 510, CNRS UMR8502/Université Paris-Sud, Centre d'Orsay, 91405 Orsay, France

Corresponding author: ^a botet@lps.u-psud.fr

Received: 15 January 2009
Revised: 13 April 2009
Published online: 8 May 2009

Abstract

The dynamics of the collective spin for Bose-Einstein condensates with nonlinear interactions, is studied within the framework of the two-component spinor. We discuss the spin resonance when the system is submitted to a periodically-modulated magnetic field at the zero temperature. In this case, the nonlinearity parameter controls the critical change between a localized and a homogeneous spin state. When the temperature is finite – or a random magnetic field is considered – the movement of the collective spin is governed by the Landau-Lifshitz-Gilbert equation, from which the complete Fokker-Planck equation is derived. This equation is the essential tool to describe the time-evolution of the probability distribution function for the collective spin. The functional integral approach is used to solve analytically examples of BEC spin behavior in a static magnetic field at finite temperature. We show how such a method can lead effectively to the complete solution of the Fokker-Planck equation for this kind of problems.