Test of the Possibility of Calculating Absorption Spectra by Mixed Quantum-Classical Methods.

摘要

Some of the most efficient methods for studying systems having a large number of degrees of freedom treat a few degrees of freedom quantum mechanically and the remainder classically. Here we examine how these methods fare when used to calculate the cross section for photon absorption by a quantum system embedded in a medium. To test the method we study a model which has two degrees of freedom and mimics the properties of an one dimensional alkali atom - He dimer. We treat the electron motion quantum mechanically and distance between the He atom and the alkali ion classically. Light absorption occurs because the electron is coupled to radiation. The calculation of the absorption cross section by quantum-classical methods fails rather dramatically: at certain frequencies the absorption coefficient is negative. By comparing with exact quantum calculations we show that this failure takes place because the time evolution of the classical variables influences the dynamics of the quantum degree of through the Hamiltonian only; important information, which a fully quantum treatment would put in the wave function, is missing.