Generalized Mean Fields for Trapped Atomic Bose-Einstein Condensates.
We describe generalized time-dependent mean-field equations for partially condensed samples of trapped and evaporatively cooled atoms. These equations give a way of investigating the various order parameters that may be present as well as the existence of a mean value of the field due to condensed atoms. Our approach provides us with a closed system of self-consistent equations for the order parameters present. The equations we derive are shown to reduce to other treatments in the literature in various limits. We also show how the equation of motion method allows us to construct a formalism that can handle the evolution of these mean fields due to two-loop kinetics.
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
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Proukakis
Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom.
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Burnett
Hartree-Fock-Bogoliubov approximation; evaporative cooling; kinetics of Bose-Einstein condensation; mean-field theory; nonlinear Schrödinger equation