Nonlinear diffusion of fermions and bosons

Abstract

A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear transformations, and the corresponding local equilibration times are deduced. Fermi-Dirac and Bose-Einstein distributions emerge as stationary solutions of the nonlinear equation. As examples, local thermalization of quarks and gluons in relativistic heavy-ion collisions, and of ultracold atoms including time-dependent Bose-Einstein condensate formation are discussed.

5 pages, 4 figures

References in corpus (4)

• Approach to equilibrium in weakly coupled nonabelian plasmas
• Solving a nonlinear analytical model for bosonic equilibration
• Time-dependent condensate fraction in an analytical model
• Time-dependent condensation of bosonic potassium

Cited by in corpus (2)

• Time-dependent condensation of bosonic potassium
• Partial Ly$\alpha$ thermalization in an analytic nonlinear diffusion model