Non‐equilibrium dynamics of open systems and fluctuation‐dissipation theorems

The Non‐Equilibrium Fluctuation‐Dissipation Theorem (NE FDT) is formulated within the Non‐Equilibrium Green Function (NEGF) formalism. The relation of this theorem to a simplified kinetic theory of non‐equilibrium dynamics of electrons in open quantum systems is discussed. The possibility of such a simplified description is first discussed on non‐equilibrium dynamics of the molecular bridge model 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. This model can be treated by using the full set of equations for NEGF, which can be solved numerically. This provides a reference framework for testing the possibility of a simpler and physically more transparent solution based on a Non‐Markovian Generalized Master Equation (GME) as an approximation of the full set of NEGF equations. The advantages and limitations of the use of the Generalized Kadanoff‐Baym Ansatz (GKBA) for this simplified description is demonstrated. The basic question is the range of applicability of this approximation. It turns out that for our specific 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. Finally, the relation of this simplified description to non‐equilibrium generalization of FDT is shown independently on the chosen model. The connection between the NEGF reconstruction equations and the non‐equilibrium version of FDT is introduced and the possible approximations of this general scheme are discussed.