The method of atomic-field collective operators in problems of interaction of atoms with a complex-structure field reservoir

The method of collective operators suitable for solving problems of non-Markovian relaxation dynamics of an atomic system of atoms in a field reservoir with 'dip'-type singularities in the spectrum of photon density of states is considered. On the basis of this method, a hierarchy of equations is constructed for collective operators; in particular, the exact solution to the problem of interaction of a two-level atom with the field is obtained for the case when two excitations are present in the system from the very beginning. The discretization procedure for the spectrum of the reservoir density of states is considered and the convergence is tested for the cases of a finite and singular density near the edge of the dip