Relaxation rates and collision integrals for Bose-Einstein condensates

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.

18 pages, 4 figures, accepted by Journal of Low Temperature Physics 7/2012

References in corpus (2)

• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• A number-conserving approach to a minimal self-consistent treatment of condensate and non-condensate dynamics in a degenerate Bose gas