Quantum transport and localization in disordered media: Liouville space dynamics with frequency-dependent dephasing

Abstract

A unified theory of quantum transport processes and spectral lineshapes in condensed phases in terms of frequency-dependent dephasing rates is developed. The effective dephasing approximation (EDA) provides a self-consistent procedure for calculating the transport properties of a quantum particle in a disordered medium. It is based on mapping the averaged Liouville space propagator into the propagator of a particle moving in an ordered lattice with an effective frequency-dependent dephasing rate. The effective dephasing rate is determined self-consistently. The Liouville equation for the averaged density matrix is isomorphic to a linearized Boltzmann equation, and the effective dephasing rate represents a generalized BGK. strong-collision operator. Applications of the EDA to the Anderson model of static disorder and to a model of dynamical disorder with a finite timescale are presented, and are shown to be in agreement with scaling theories. The frequency-dependent dephasing which determines the transport processes is found to be much more sensitive to quantum localization than the dephasing which enters into the calculation of optical lineshapes and densities of states.