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
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.
PACS: 03.75.Mn – Multicomponent condensates; spinor condensates / 05.10.Gg – Stochastic analysis methods
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009