SCATTERING, DISSIPATION, AND TRANSPORT IN MESOSCOPIC SYSTEMS

A theoretical study of dissipative scattering in mesoscopic systems is presented. Within the single electron and localized phonon approximations, exact expressions for the transmission and reflection probabilities between the various leads and channels are derived in terms of dressed two-particle Green's functions. These general results are obtained through two different procedures: one approach is based on a direct study of the microscopic stationary scattering amplitudes while in a second method the reduced density matrix of a scattered wave packet is analyzed. In both approaches the phonon bath degrees of freedom are traced out in such a way that an effective description of the electron dissipative dynamics emerges. The scattering probabilities are shown to satisfy symmetry relations which exactly account for the presence of a dissipative thermal bath. A lattice formulation of the calculational method is also presented, and an explicit proof of unitarity is obtained by invoking the continuity equation. By introducing time-ordering in the Keldysh contour, a diagrammatic perturbation theory in the electron-phonon interaction is developed. Unitarity is shown to be automatically preserved to all orders in perturbation theory. The use of diagrams is illustrated by applying them to some simple cases involving one- and two-phonon processes. Finally, a discussion is presented on the computation of the current from the inelastic scattering probabilities. The existence of an ambiguity in the assignment of quantum statistical factors to the outgoing scattering channels is pointed out. It is argued that a more consistent picture is obtained if no statistical restrictions are explicitly introduced in the electron final states. The novel formulation which is presented here provides a theoretical framework for quantitative studies of the interplay between quantum interference and dissipation in the transport properties of very small structures. © 1992 Academic Press, Inc. All rights reserved.