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10 - Kinetics of Bose–Einstein Condensate Formation in an Interacting Bose Gas

Published online by Cambridge University Press:  15 December 2009

YU. Kagan
Affiliation:
Department of Superconductivity and Solid State Physics Kurchatov Institute 123182 Moscow Russia
A. Griffin
Affiliation:
University of Toronto
D. W. Snoke
Affiliation:
University of Pittsburgh
S. Stringari
Affiliation:
Università degli Studi di Trento, Italy
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Summary

Abstract

The kinetics of the formation of coherent correlation properties associated with Bose condensation is studied in detail. The evolution of a nonequilibrium state with no “condensate-seed” is related to a hierarchy of relaxation times. At the first stage, a particle flux in energy space toward low energies sets in. The evolution in this case is described by a nonlinear Boltzmann equation, with a characteristic time given by interparticle collisions. When the particles which will later form the condensate have a kinetic energy which is less than the potential energy, a quasicondensate starts to form. In this stage, fluctuations of the density (but not of the phase) are suppressed and short-range coherent correlation properties are governed by the equation of motion for a quasiclassical complex field. The next stage is connected with the formation of the long-range order. The time for forming topological order and therefore genuine superfluidity proves to be dependent on the system size. The off-diagonal long-range order, arising after the attenuation of long-wave phase fluctuations, has a size-dependent relaxation time as well.

Introduction

The problem of Bose–Einstein Condensation (BEC) kinetics, being interesting in itself, has acquired a special significance in connection with experimental efforts to observe this condensation in a number of systems with particles with a finite lifetime. Such systems include spin-polarized atomic hydrogen [1], excitons [2] and biexcitons [3] in semiconductors and, more recently, laser-cooled atomic systems [4].

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Publisher: Cambridge University Press
Print publication year: 1995

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