Transport in molecular states language: Generalized quantum master equation approach

Abstract

A simple scheme, capable of treating transport in molecular junctions in the language of many-body states, is presented. By introducing an ansatz in Liouville space, similar to the generalized Kadanoff-Baym approximation, a quantum master equation ͑QME͒-like expression is derived starting from the exact equation of motion for Hubbard operators. Using an effective Liouville space propagation, a dressing similar to the standard diagrammatic one is proposed. The scheme is compared to the standard QME approach and its applicability to transport calculations is discussed.

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

“…58,[67][68][69][70][71][72][73][74][75][76][77][78] However, only very few of them are applicable to the present model. This is because the model involves vibronic coupling to a relatively large number of vibrational modes in nonequilibrium.…”

“…To this end, a variety of theoretical approaches have been developed and employed, including scattering theory, [50][51][52][53][54][55][56][57] nonequilibrium Green's function approaches, [58][59][60][61][62][63][64][65][66] and master equation methods. 58,[67][68][69][70][71][72][73][74][75][76][77][78] Although much physical insight has been obtained by the application of these methods, all these approaches involve significant approximations. For example, nonequilibrium Green's function (NEGF) methods and master equation approaches are usually based on (self-consistent) perturbation theory and/or employ factorization schemes.…”

Lindblad equation and its semiclassical limit of the Anderson-Holstein model

“…In the perspective of quantum master equation, which is mostly related to the current work, the quantum master equation in Redfield flavor for Anderson-Holstein model has been derived in [14][15][16]. The semiclassical limit of the Redfield equation, known as the classical master equation (CME), has been considered in [5], which also proposed a numerical method based on surface hopping.…”

“…Anderson-Holstein model, since introduced, has been widely studied using various theoretical and numerical approaches, for instance, the Green's function approach [6,7], equation-of-motion method [8,9], quantum Monte Carlo method [10], semi-classical approximation [11,12], non-crossing approximation [13] and by using quantum master equations [5,[14][15][16][17][18][19]. In the perspective of quantum master equation, which is mostly related to the current work, the quantum master equation in Redfield flavor for Anderson-Holstein model has been derived in [14][15][16].…”

Simulation of optical response functions in molecular junctions

“…is the Liouville space retarded Green function [71], and L is the Liouvillian. Fourier transform of the retarded Green function is…”