Stochastic Liouville Equation for Weakly Driven System. I: -- TCL Equation and Its Application to a Quantal Oscillator --

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Abstract
A time-convolutionless stochastic equation is derived from a stochastic quantal Liouville equation for a weakly driven system under random perturbations with an arbitrary initial condition, in the linear approximation for the external driving field. This equation is applied to a quantal oscillator interacting weakly with its surroundings under decoupled initial condition, up to second order in powers of random perturbations. The results are compared with those derived from the time-convolution equation in the conventional Markoffian approximation, and with those derived by the method of second-order relaxation theory and Kubo's theory. It is shown that the effects of interference of the external driving field and the random interaction with the surroundings enhance the line shape of a power spectrum over the Lorentzian at the resonance region. Validity of the second-order perturbation calculations is discussed.

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