Dynamics of spinor condensates and stochastic approach |
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Authors: | H Kuratsuji and R Botet |
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Institution: | (1) Department of Physics, Ritsumeikan University-BKC, Noji-Hill, Kusatsu City 525-8577, Japan;(2) Laboratoire de Physique des Solides Bat. 510, CNRS UMR8502/Université Paris-Sud, Centre d’Orsay, 91405 Orsay, France |
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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. |
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Keywords: | PACS" target="_blank">PACS 03 75 Mn Multicomponent condensates spinor condensates 05 10 Gg Stochastic analysis methods |
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