1202.3418 (Erich D. Gust et al.)

Collision Integrals in the Kinetic Equations of dilute Bose-Einstein
Condensates    [PDF]

Erich D. Gust, L. E. Reichl

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.

View original: http://arxiv.org/abs/1202.3418