  I study the time evolution of the density matrices of quantum Fermi systems
interacting with classic external Fermi fields. This interaction either changes
the temperature of the system or it affects the density of particles. For
relativistic Dirac fermions, variations of temperature lead to creation
(annihilation) of particle - antiparticle pairs. The change of the density (or
of the chemical potential) indicates the existence of the incoming (outgoing)
flux of fermions from (to) the bath. These changes are independent for the
different modes and in order to model the thermalization one should adjust the
spectrum of the noise. The linear time dependences of the densities of
particles are characteristic for all the processes.
