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.
Categories: cond-mat.quant-gas