ar X iv : c on d - m at / 9 71 01 28 v 1 1 4 O ct 1 99 7 Damping of low - energy excitations of a trapped Bose condensate at finite temperatures

We present the theory of damping of low-energy excitations of a trapped Bose 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 non-spherical traps. The damping rates of the lowest excita-tions, 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. After the discovery of Bose-Einstein condensation (BEC) [1–3], one of the major directions in the physics of ultra-cold gases has been the investigation of collective many-body effects. Especially interesting is the behavior of low-energy collective excitations of a trapped con-densate. The JILA [4,6] and MIT [5,7] experimental studies of the excitations related to shape oscillations of the condensate show that these excitations are damped and provide us with interesting results on the temperature dependence of the damping rates and frequency shifts. In this letter we develop the theory of damping of excitations of a trapped condensate in the Thomas-Fermi regime at finite temperatures, where the presence of a thermal component is important. We confine ourselves to the damping of low-energy excitations, i.e., the excitations with energies E ν ≪ µ, where µ is the chemical potential, and consider temperatures T ≫ ¯ hω (ω is the characteristic trap frequency) ranging almost up to the BEC 1