Semiclassical treatment of non-Markovian dissipative quantum dynamics

Any realistic system is coupled to its environment even if this coupling is very weak. The influence of the environment can result in dissipation of energy as well as decoherence of states in the system. Both effects have to be taken into account to accurately describe the time evolution of a state prepared in the system. A model system for the study of these effects is a single oscillator, linearly coupled to a bath of oscillators with a fixed temperature. The dynamics of the heat bath is treated using the influence functional formalism. We show numerical results for the system under the influence of the heat bath using semiclassical techniques in initial value representation. Issues arising during such calculations are discussed