RELATION BETWEEN METHOD OF TCL EQUATION WITH EXTERNAL TERMS AND RELAXATION METHOD - QUANTAL BATH MODEL

The relation between the method of TCL equation with external driving terms and the relaxation method is discussed analytically in the quantal bath model. It is shown that the interference term in the former method gives the part of second order in powers of the system-bath interaction in the Kubo formula, and that the former method is simpler than the latter method. It is also shown that the relaxation method neglects the low temperature effects which are given by the first part of interference term, and that the relaxation method in the narrowing limit neglects the effects of the interference term completely. The general form of admittance for the case of decoupled initial condition is given by the method of TCL equation with external driving terms, and can be equal to that for the case of thermal equilibrium initial condition. The above facts are verified by applying to a quantal oscillator. Validity of the second-order perturbation calculations is discussed.