Relaxation rates and collision integrals for Bose-Einstein condensates

Erich D. Gust; L. E. Reichl

doi:10.1007/s10909-012-0675-7

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arXiv · 1207.6591

Relaxation rates and collision integrals for Bose-Einstein condensates

Erich D. Gust·L. E. Reichl

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Abstract

Near equilibrium, the rate of relaxation to equilibrium and the transport properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC) are determined by three collision integrals, $\mathcal{G}^{12}$, $\mathcal{G}^{22}$, and $\mathcal{G}^{31}$. All three collision integrals conserve momentum and energy during bogolon collisions, but only $ \mathcal{G}^{22}$ conserves bogolon number. Previous works have considered the contribution of only two collision integrals, $ \mathcal{G}^{22}$ and $ \mathcal{G}^{12}$. In this work, we show that the third collision integral $ \mathcal{G}^{31}$ makes a significant contribution to the bogolon number relaxation rate and needs to be retained when computing relaxation properties of the BEC. We provide values of relaxation rates in a form that can be applied to a variety of dilute Bose-Einstein condensates.

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Erich D. Gust, L. E. Reichl. 2012-07-27. Relaxation rates and collision integrals for Bose-Einstein condensates. https://doi.org/10.1007/s10909-012-0675-7

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