Publication at Faculty of Mathematics and Physics |

2021

This article addresses the problem of an efficient description of the transient electron transport in (primarily small open) quantum systems out of equilibrium. It provides an overview and critical review of the use of causal Ansatzes with the accent on derivation of (quantum) transport equations from the standard Kadanoff-Baym (KB) equations for the non-equilibrium Green's functions (NEGF).

The family of causal Ansatzes originates from the well-known Generalized Kadanoff-Baym Ansatz (GKBA). The Ansatz technique has been fairly successful in practice.

Recently, the scope of the method has been extended towards more "difficult" cases and its success can be assessed more precisely. This general picture is demonstrated and analyzed in detail for a variant of the generic molecular island model, an Anderson impurity linked between two bulk metallic leads by tunneling junctions.

First, the KB equations are reduced to a non-Markovian generalized master equation (GME) by means of a general causal Ansatz. Further reduction to a Markovian master equation is achieved by partly relaxing the strictly causal character of the theory.

For the model narrowed down to ferromagnetic leads, the transient currents are spin polarized and the tunneling functions have a complex spectral structure. This has prompted deriving explicit conditions for the use of an Ansatz.

To extend the applicability range of the GME, approximate vertex corrections to the Ansatz were introduced and used with success. Finally, the relation of the GME description to possible non-equilibrium generalizations of the fluctuation-dissipation theorem is shown, extended beyond the present model within the NEGF formalism and physically interpreted in terms of a simplified kinetic theory of non-equilibrium electrons in open quantum systems.