Mean field Ehrenfest quantum/classical simulation of vibrational energy relaxation in a simple liquid

We give a detailed account of the statistical mechanical properties of the mean field Ehrenfest quantum/classical method as applied to liquid phase vibrational energy transfer using a simple harmonic oscillator model Hamiltonian. Depending on the shape of the initial quantum wave packet, a (partial) breakdown of detailed balance is observed, where the frictional response of the classical bath is only correlated to quasiclassical features of the evolving quantum state, i.e., a classical-like fluctuation-dissipation theorem holds. Only in the case of a coherent initial state (minimum uncertainty wave packet) does the mean field method produce physically meaningful results, namely, exponential relaxation (τ=τ_cl) towards a quasiclassical equilibrium.