Stochastic classical trajectory approach to relaxation phenomena. III. Comparison of trajectory results to quantum mechanical perturbation theory

A simple model representing an impurity oscillator coupled anharmonically to a lattice is examined both by quantum mechanical perturbation theory and by stochastic classical trajectory simulations. Energy relaxation rates are computed as a function of temperature. Classical and quantum relaxation rates are found to agree well at high temperatures but, as expected, diverge drastically at low temperatures. If zero-point motion of the lattice is incorporated into the classical calculation, classical and quantum relaxation rates agree quite well for all temperatures, even for T→0. This suggests that the stochastic classical trajectory method can provide an accurate description of relaxation phenomena even at very low temperatures.