(in press) The Influence Functional from a Bath of Coupled Time-Dependent Harmonic Oscillators

The influence functional from a heat bath consisting of coupled harmonic oscillators of time-dependent frequency and coupling con-stants is derived. Like its time-independent counterpart, the present in-fluence functional also involves the force-force autocorrelation function of the bath. Any system in real world is hardly separated from the environment. Due to the interaction with a large number of environmental degrees of freedom which act as a heat bath, the dynamics of the sys-tem becomes dissipative. In classical mechanics, the dynamics of the system is for practical purposes stochastic and is well described by the Langevin equation. By contrast, the quantum behavior of dissi