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arXiv:cond-mat/9911238

Damping of low-energy excitations of a Bose-condensed gas in the hydrodynamic regime

Peter O. Fedichev, A. E. Muryshev, Gora V. Shlyapnikov

Published Nov 16, 1999• 0 citations
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Abstract

We develop a theory to describe the damping of elementary excitations of a Bose-condensed gas in the hydrodynamic regime for the thermal cloud. We discuss second sound in a spatially homogeneous gas and the lowest excitations of a trapped condensate.
DOI
10.48550/arxiv.cond-mat/9911238

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Collective excitations of a dilute Bose gas were probed above and below the Bose-Einstein condensation temperature. The temperature dependencies of the frequency and damping rates of condensate oscillations indicate significant interactions between the condensate and the thermal cloud. Hydrodynamic oscillations of the thermal cloud analogous to first sound were observed. An out-of-phase dipolar oscillation of the thermal cloud and the condensate was also studied, analogous to second sound. The excitations were observed in situ using nondestructive imaging techniques.
We present the theory of damping of low-energy excitations of a trapped Bose-Einstein condensate at finite temperatures, where the damping is provided by the interaction of these excitations with the thermal excitations. We emphasize the key role of stochastization in the behavior of the thermal excitations for damping in nonspherical traps. The damping rates of the lowest excitations, following from our theory, are in fair agreement with the data of recent JILA and MIT experiments. The damping of quasiclassical excitations is determined by the condensate boundary region, and the result for the damping rate is drastically different from that in a spatially homogeneous gas.
Griffin, Wu and Stringari have derived the hydrodynamic equations of a trapped dilute Bose gas above the Bose-Einstein transition temperature. We give the extension which includes hydrodynamic damping, following the classic work of Uehling and Uhlenbeck based on the Chapman-Enskog procedure. Our final result is a closed equation for the velocity fluctuations δvδvδv which includes the hydrodynamic damping due to the shear viscosity ηηη and the thermal conductivity κκκ. Following Kavoulakis, Pethick and Smith, we introduce a spatial cutoff in our linearized equations when the density is so low that the hydrodynamic description breaks down. Explicit expressions are given for ηηη and κκκ, which are position-dependent through dependence on the local fugacity when one includes the effect of quantum degeneracy of the trapped gas. We also discuss a trapped Bose-condensed gas, generalizing the work of Zaremba, Griffin and Nikuni to include hydrodynamic damping due to the (non-condensate) normal fluid.