To account for the thermalization of, and the time-dependent Bose-Einstein condensate (BEC) formation in ultracold quantum gases, a nonlinear boson diffusion equation (NBDE) is presented. It is one of the few nonlinear partial differential equations that can be solved analytically. The solution method is explained, and the outcome is shown to agree with numerical results. The model results are compared with recent time-dependent BEC formation data for potassium-39 from Cambridge University at various interaction strengths (s-wave scattering lengths), confirming the validity and usefulness of the nonlinear diffusion model, which has also been applied to the fast thermalization of gluons in relativistic heavy-ion collisions.
Organized by: Paulo Brás, Paulo Silva, Jaime Silva