Comment on the phase problem in the semiclassical Langevin simulations of the Davydov system

This article deals with a problem that arises in the existing treatments of the nonequilibrium regime of mixed quantum/classical systems. It is known that a straightforward application of standard Langevin methods to such systems leads to a violation of the a priori random phases postulate of quantum statistical mechanics. Through numerical analysis, we evaluate the quantitative effects such approximation procedures have on the thermal equilibrium behaviour of the semiclassical Davydov model. We find that the strength of localized states at finite temperature is underestimated by the classical thermalization schemes. We also use simulations with different Langevin-type schemes to illustrate the order of magnitude that can be involved when the nature of the thermal bath is changed. These results indicate that transient properties, such as the lifetime of localized states, obtained from simulations with the classical thermalization schemes, should be considered as underestimates of the true values.