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Laser Physics

Kinetic equation for a weakly nonideal Bose gas

Е. А. Титов

Published Aug 30, 2006• 1 citation
Publisher

Abstract

A kinetic equation for a weakly nonideal Bose gas is derived in the range where the thermal wavelength (λT) is less than or on the order of the mean interatomic distance (r 0). The case when λT > r 0 is discussed.
DOI
10.1134/s1054660x06090118

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The Bogoliubov theory of a uniform weakly-nonideal Bose-Einstein condensate leads to a divergent expression for the kinetic energy of atoms. However, the latter can be determined provided that the dependence of the scattering length on atomic mass is known. The explicit expressions are derived for the kinetic energy through parameters that specify interatomic interaction. The kinetic energy of condensate atoms noticeably exceeds the total energy. Numerical data are presented for Rb-87 and Na-23 condensates.
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We consider the ordering kinetics in a strongly non-equilibrium state of a (weakly) interacting Bose gas, characterized, on one hand, by large occupation numbers, and, on the other hand, by the absence of long-range order. Up to higher-order corrections in inverse occupation numbers, the evolution is described by non-linear Schrodinger equation with a turbulent initial state. The ordering process is rather rich and involves a number of qualitatively different regimes that take place in different regions of energy space. Specially addressed is the case of evolution in an external potential.