Time-dependent condensate formation in ultracold atoms with energy-dependent transport coefficients

Time-dependent Bose-Einstein condensate formation in ultracold atoms is investigated in a nonlinear diffusion model. For constant transport coefficients, the model has been solved analytically. Here, we extend it to include energy-dependent transport coefficients and numerically solve the nonlinear equation. Our results are compared with the earlier analytical model for constant transport coefficients, and with recent deep-quench data for ${}^{39}\mathrm{K}$ at various scattering lengths. Some nonphysical predictions from the constant-coefficient model are resolved using energy-dependent drift and diffusion.