A Generalized Equation of Motion for the Lineqr Response. II: Simple Application to a Quantal Oscillator
Mizuhiko Saeki · Progress of Theoretical Physics · 1985
The time-convolutionless equation of motion for the linear response derived in a previous paper is applied to a simple system of a quantal oscillator. This system is assumed to be interacting weakly with its surroundings (heat bath). The two cases for the initial state of the total system are considered. One case is that the oscillator and heat bath are in thermal equilibrium, and another is that these two systems are uncoupled and in each thermal equilibrium at the same temperature. The operator forms of equations are transcribed into the c-number ones by the phase-space method. The equations of motion for the expectation values of the boson operator and boson number operator are derived from the c-number equations and are solved for the case of a non-adiabatic oscillator-bath interaction. The results are compared with the ones in the conventional Markoffian approximation.