Coupled quasiparticle-boson systems: The semiclassical approximation and discrete nonlinear Schrödinger equation

Abstract

The validity of the semiclassical approximation is studied for a system comprising one quasiparticle coupled to a boson degree of freedom. Using a two-site Holstein model as an example, it is shown that the semiclassical approximation becomes exact in a nontrivial adiabatic limit. Furthermore, in the model's polaron regime, there exists a hierarchy of time scales that rationalizes the quantum dynamics of the Holstein model. For the single-mode case considered, the discrete nonlinear Schr\"odinger equation is found to be valid only in a highly limited antiadiabatic regime.