The stochastic Gross-Pitaevskii equation

Authors: Gardiner, C.W.1; Anglin, J.R.2; Fudge, T.I.A.3

Source: Journal of Physics B: Atomic, Molecular and Optical Physics, Volume 35, Number 6, 2002 , pp. 1555-1582(28)

Publisher: IOP Publishing

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We show how to adapt the ideas of local energy and momentum conservation in order to derive modifications to the Gross-Pitaevskii equation which can be used phenomenologically to describe irreversible effects in a Bose-Einstein condensate. Our approach involves the derivation of a simplified quantum kinetic theory, in which all processes are treated locally. It is shown that this kinetic theory can then be transformed into a number of phase-space representations, of which the Wigner function description, although approximate, is shown to be the most advantageous. In this description, the quantum kinetic master equation takes the form of a Gross-Pitaevskii equation with noise and damping added according to a well defined prescription - an equation we call the stochastic Gross-Pitaevskii equation. From this, a very simplified description we call the phenomenological growth equationcan be derived. We use this equation to study (i) the nucleation and growth of vortex lattices, and (ii) nonlinear losses in a hydrogen condensate, which it is shown can lead to a curious instability phenomenon.

Document Type: Miscellaneous

Affiliations: 1: School of Chemical and Physical Sciences, Victoria University, Wellington, New Zealand 2: Center for Ultracold Atoms, MIT 26-251, 77 Massachusetts Ave., Cambridge, MA 02139, USA 3: Wilton Research Institute, Wilton, Wellington, New Zealand

Publication date: January 1, 2002

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