Memory effects in transport theory: An exact model

Abstract

We consider the propagation of electromagnetic radiation through a medium consisting of noninteracting harmonically bound electrons in a blackbody-radiation heat bath. An exact result for the ac conductivity is obtained, which differs from the well-known Drude-Lorentz result by the presence of memory (non-Markovian) effects. In particular, the absorption line is considerably changed in shape, especially away from resonance. Our approach---which is based on the use of a generalized quantum Langevin equation---transcends the particular model discussed as it enables the conductivity to be calculated directly, in contrast to Kubo-type calculations which require the evaluation of correlation functions as an intermediate step. Furthermore, the model itself should prove useful as a testing ground for the various quantum theories of conductivity which are presently being explored for possible use in studies of submicron semiconductor devices.