Quantum master-equation approach to quantum transport through mesoscopic systems

Abstract

For quantum transport through mesoscopic systems, a quantum master-equation approach is developed in terms of compact expressions for the transport current and the reduced density matrix of the system. The present work is an extension of Gurvitz's approach for quantum transport and quantum measurement, namely, to finite temperature and arbitrary bias voltage. Our derivation starts from a second-order cumulant expansion of the tunneling Hamiltonian; then follows the conditional average over the electrode reservoir states. As a consequence, in the usual weak-tunneling regime, the established formalism is applicable for a wide range of transport problems. The validity of the formalism and its convenience in application are well illustrated by a number of examples.

Master equation approach to transient quantum transport in nanostructures incorporating initial correlations

“…14,[16][17][18][19] In the steady-state quantum transport regime, the famous Landauer-Büttiker formula 9 has been widely utilized to calculate successfully various transport properties in semiconductor nanostructures. 4,5 In the Landauer-Büttiker formula, the transport current is given in terms of a simple transmission coefficient obtained from the single-particle scattering matrix.…”

“…16 An interesting development of master equations in quantum transport systems is the hierarchical expansion of the equations of motion for the reduced density matrix, 17 which provided a systematical and also quite useful numerical calculation scheme to quantum transport.…”

Super-fermion representation of quantum kinetic equations for the electron transport problem

“…Recent progress in the development of kinetic equations for the electron transport presents a significant promises in this direction. [39][40][41][42][43][44][45][46][47] Although to fully engage transport kinetic equations with the high level electronic structure calculations we need to transform them to the familiar language of second quantization, creation and annihilation operators, normal ordering, Fock space and vacuum. In this paper paper we develop a systematic scheme to convert and solve quantum kinetic equations in the language of the advanced quantum chemistry.…”

Transport in molecular states language: Generalized quantum master equation approach

“…Among these approaches, one can mention scattering theory, 7 rate equations, [8][9][10][11][12][13][14] quantum master equations ͑QMEs͒, [15][16][17][18][19][20][21] and the nonequilibrium Green's-function ͑GF͒-based schemes. [22][23][24] Each of these has its own limitations.…”