A generalized stochastic liouville equation. Non-Markovian versus memoryless master equations

The interrelation between the well-known non-Markovian master equation and the new memoryless one used in the previous paper is clarified on the basis of damping theory. The latter equation is generalized to include cases in which the Hamiltonian or the Liouvillian is a random function of time, and is written in a form feasible for perturbational analysis. Thus, the existing stochastic theory in which those cases mentioned above are discussed is equipped with a more tractable basic equation. Two problems discussed in the previous paper, i.e., the random frequency modulation of a quantal oscillator and the Brownian motion of a spin, are treated from the viewpoint of the stochastic theory without such explicit consideration of external reservoirs as was taken in the previous paper.