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arXiv:cond-mat/0508684

Kinetic energy of uniform Bose-Einstein condensate

E. E. Nikitin, Лев П. Питаевский

Published Aug 29, 2005• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.cond-mat/0508684

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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.
The viscosity of a dilute Bose–Einstein condensate is obtained for a range of temperatures and densities. The kinetic equation used to derive the viscosity is based on Bogoliubov mean field theory and is a Boltzmann-like equation for the Bogoliubov excitations in the condensate. The viscosity can be assigned a numerical value for any gas for which the mass and scattering length are known. The viscosity decreases slowly as the temperature is decreased, but at low temperature (around 0.01 T c ), begins to show a much more rapid decrease with decreasing temperature. This interesting behavior of the viscosity is related to the behavior of the eigenvalues of the bogolon collision operator at these low temperatures.
The evolution equation of a weakly interacting boson system is derived. The model includes the interaction between the atoms in the condensate and the surrounding gas of noncondensed particles. The Bogoliubov transformation is introduced in a full quantum context and the scattering kernel between dressed particles and the condensate phase is obtained. The final system is expressed by the Boltzmann evolution equation for noncondensed particles coupled to the Gross-Pitaevskii equation for the condensate. We consider an out-of-equilibrium situation that induces a fast production of condensed particles. We apply our model to study the condensation dynamics of positronium atoms by evaporation.
It is known that for a weakly interacting Bose-Einstein condensate (BEC), the assumption of a two-body $\ensuremath{\delta}$ interaction described by a constant coupling strength gives rise to a divergent ground-state energy. A similar divergence occurs in the spinor condensate in which the spin-spin interaction is included in addition to the repulsive $\ensuremath{\delta}$ interaction. In this paper, we examine, in the standard Bogoliubov approximation, the ground-state energy of a homogeneous spinor BEC with hyperfine spin f=1.f=1.f=1. The renormalized coupling constants are calculated and expressed in terms of the bare ones using the standard second-order perturbation method. With these renormalized coupling constants, we show that the ultraviolet divergence of the ground-state energy can be exactly eliminated.