Markov limit for a quantum particle interacting with a Fermi gas

A quantum particle interacting with the Fermi gas is studied. The interaction represents the analogue of the dipole approximation to the interaction between the atom and electromagnetic field. Existence of the weak interaction limit is proved which is described by the quantum-dynamical semi-group on the observable algebra. The structure of this semi-group and the convergence to the equilibrium state is investigated and the uniqueness of the invariant state is proved.