Collision Integrals in the Kinetic Equations of dilute Bose-Einstein   Condensates
  We derive the mean field kinetic equation for the momentum distribution of Bogoliubov excitations (bogolons) in a spatially uniform Bose-Einstein condensate (BEC), with a focus on the collision integrals. We use the method of Peletminksii and Yatsenko rather than the standard non-equilibrium Green's function formalism. This method produces three collision integrals ${\cal G}^{12}$, ${\cal G}^{22}$ and ${\cal G}^{31}$. Only ${\cal G}^{12}$ and ${\cal G}^{22}$ have been considered by previous authors. The third collision integral ${\cal G}^{31}$ contains the effects of processes where one bogolon becomes three and vice versa. These processes are allowed because the total number of bogolons is not conserved. Since ${\cal G}^{31}$ is of the same order in the interaction strength as ${\cal G}^{22}$, we predict that it will significantly influence the dynamics of the bogolon gas, especially the relaxation of the total number of bogolons to its equilibrium value. 
Erich D. Gust, L. E. Reichl
cond-mat.quant-gas quant-ph