This area of research deals with problems of the proper description of electron dynamics of quantum systems out of equilibrium from a finite time initial state over the transient period to the long time asymptotic. In general, the dependence on initial and boundary conditions as well as system interactions and external fields must be included into the description. The standard tool, Non-Equilibrium Green’s Functions (NEGF), can be simplified, under some conditions, to Non-Markovian Generalized Master Equations (GME) for single particle density. The conventional approximation for this purpose, based on the Generalized Kadanoff-Baym Ansatz (GKBA), has been fairly successful in practice, but exact criteria for its validity are so far missing.
The possibility of such a simplified description is tested on non-equilibrium dynamics of various versions of the molecular bridge model. For instance, this approach can be represented by calculations of transient magnetic currents between two ferromagnetic electrodes linked by tunneling junctions to a molecular size island of an Anderson local center type. The transient studied is a free relaxation of an initial state created by suddenly switching on of both junctions. The transient currents are spin polarized and the tunneling functions have a complex spectral structure. This model can be treated by using the full set of equations for NEGF, which can be solved numerically. This provides us a reference framework for testing the possibility of a simpler and physically more transparent solution based on a non-Markovian GME as an approximation of the full set of NEGF equations, which can be derived by using the GKBA. The advantages and limitations of the use of GKBA for this simplified description has been demonstrated. It turns out that for this model the decisive feature is the spectral structure of the tunneling functions of both electrodes and their positioning with respect to the island level depending on the bias and the exchange splitting. When these tunneling functions have a complex spectral structure, an improved GME, based on the use of a corrected GKBA, is derived. The limitations and possible improvements of the GKBA approximation, as well as an improved GME, based on the use of a corrected GKBA, will be further investigated.
The following intention is to investigate various forms of GKBA like approximations and related transport equations for open condensed matter systems. Under some conditions non-equilibrium Fluctuation-Dissipation (FD) theorems can be formulated within the NEGF formalism. The long time aim is to use these theorems for formulation of a simplified transport theory of non-equilibrium dynamics of electrons in quantum systems and investigate the range of validity of such effective theories.