Quantum dynamics of a strongly coupled dissipative system toward thermal equilibrium I

The quantum dynamics of a strongly coupled dissipative system toward thermal equilibrium is investigated by means of the the Jaynes-Cummings model with relaxation mechanisms. Our relaxation model ensures that the coupled system evolves in time to the correct canonical distribution in thermal equilibrium. The quantal master equation is expended in terms of the eigenstates of the whole coupled system. The time evolution of the elements of the reduced density matrix is described by the vector tri-diagonal differential equation. The relaxation process reveals itself through the dynamics of these elements resulting in the canonical distribution. Quantum characteristics are found both in the short time regime and the long time regime. The short time regime is characterized by the decoherence process, which represents the phase relaxation, whereas the long time relaxation process is dominated by the diagonal process of the energy relaxation