Quantum dissipative master equations: Some exact results

Abstract

The results for two quantum dissipative master equations were derived with the help of quantum characterstics functions. These equations included disspative Liouvillian operators of the Lindblad type corresponding to two forms of dissipation mechanisms. The evoluton of level populations for an oscillator in a coherent state with certain displacement in undamped regime was also studied. The analysis suggested that the Hamiltonian represented the excited manifold with one primary oscillator in the Brownian oscillator model. The study also revealed that if the bath temperature was sufficiently high, the vibrational manifold could reach a Boltzmann-type distribution before it came ito full thermal equilibrium with the surrounding bath.