Transport theory of interacting mesoscopic systems: A memory-function approach to charge-counting statistics

Abstract

We address the subtle problem of formulating mesoscopic transport phenomena in the language of many-body physics. We propose a microscopic description in which the whole system (sample, leads, and detectors) is given fully-quantum-mechanical treatments. The dynamics of the system is obtained from the projection, or memory-function, formalism of nonequilibrium statistical mechanics combined with recent prescriptions for measurements that are extended in the time domain. The associated irreversible quantum dynamics contains an intrinsic doubling of the degrees of freedom identical to the real-time path-integral representation of the Keldysh formalism. We derive a simple formula relating the generating function of the charge-counting statistics to the single-particle matrix Green's function of the interacting system, thereby generalizing the Levitov-Lesovik functional determinant formula. We report an interesting sample-leads duality in our description, which has a simple interpretation in the regime of noninteracting particles, thus establishing the equivalence between the Green's-function technique and the random scattering-matrix approach. We discuss the physical conditions, within the present scheme, for the validity of the Landauer-Buttiker description of mesoscopic transport. We conclude by providing an exact solution for the problem of charge transfer into a noninteracting ballistic cavity in the presence of a periodic time-dependent voltage, using the supersymmetry method.