Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation

Bradley, A. S., Blakie, P. B. and Gardiner, C. W. (2005) Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation. Journal of Physics B: Atomic Molecular and Optical Physics, 38 23: 4259-4280. doi:10.1088/0953-4075/38/23/008


Author Bradley, A. S.
Blakie, P. B.
Gardiner, C. W.
Title Properties of the stochastic Gross-Pitaevskii equation: finite temperature Ehrenfest relations and the optimal plane wave representation
Journal name Journal of Physics B: Atomic Molecular and Optical Physics   Check publisher's open access policy
ISSN 0953-4075
Publication date 2005-01-01
Sub-type Article (original research)
DOI 10.1088/0953-4075/38/23/008
Volume 38
Issue 23
Start page 4259
End page 4280
Total pages 22
Editor J-M. Rost
Place of publication United Kingdom
Publisher Institute of Physics Publishing
Collection year 2005
Language eng
Subject C1
240301 Atomic and Molecular Physics
780102 Physical sciences
Abstract We present Ehrenfest relations for the high temperature stochastic Gross-Pitaevskii equation description of a trapped Bose gas, including the effect of growth noise and the energy cutoff. A condition for neglecting the cutoff terms in the Ehrenfest relations is found which is more stringent than the usual validity condition of the truncated Wigner or classical field method-that all modes are highly occupied. The condition requires a small overlap of the nonlinear interaction term with the lowest energy single particle state of the noncondensate band, and gives a means to constrain dynamical artefacts arising from the energy cutoff in numerical simulations. We apply the formalism to two simple test problems: (i) simulation of the Kohn mode oscillation for a trapped Bose gas at zero temperature, and (ii) computing the equilibrium properties of a finite temperature Bose gas within the classical field method. The examples indicate ways to control the effects of the cutoff, and that there is an optimal choice of plane wave basis for a given cutoff energy. This basis gives the best reproduction of the single particle spectrum, the condensate fraction and the position and momentum densities.
Keyword Optics
Physics, Atomic, Molecular & Chemical
Bose-einstein Condensation
Quantum Kinetic-theory
Classical-field Approximation
Master Equation
Dynamics
Gases
Vortices
Systems
Growth
Bosons
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 17:04:20 EST