Equilibration in fermionic systems
Highlights: •Local equilibration in finite fermion systems is based on a nonlinear diffusion equation. •The fermionic diffusion equation is solved analytically in closed form. •The exact solutions agree with the numerical results. •Particle-number and energy conservation are shown to be fulfilled. •The model is applied to hadrons at low energies, and relativistic quarks. -- Abstract: The time evolution of a finite fermion system towards local statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The solutions of this fermionic diffusion equation are rederived in closed form, evaluated exactly for simplified initial conditions, and applied to hadron systems at low energies in the MeV-range, as well as to quark systems at relativistic energies in the TeV-range where antiparticle production is abundant. Conservation laws for particle number including created antiparticles, and for the energy are discussed.