Relaxation theory of a strongly coupled system

A model of relaxation is presented for the Jaynes-Cummings model. Interaction between the relevant system and the reservoir is introduced to exchange mutual energies. After elimination of reservoir variables a quantal master equation is derived. This is expanded in terms of eigenstates of the total Hamiltonian of the relevant system. A set of basic equations are obtained in a vector tri-diagonal form which determines time evolution of components of the density matrix. The resulting basic equations become solvable and can be used even for strong interaction in the relevant subsystems. Moreover, these equations evolve in time to the correct equilibrium values