Dynamics of mesoscopic systems: Non-equilibrium Green's functions approach

Developments in technologies and experiments enable us to observe dynamical behavior of small quantum systems under conditions when it is sensitive to system parameters, internal interactions, the environment and the external time-dependent fields. This contribution deals with the status and perspectives of description of such non-equilibrium quantum many body systems using non-equilibrium Green's functions.This approach describes time development of the many-body system out of equilibrium from its initial state over its transient dynamics to its long time asymptotic evolution. The early stages of the transient evolution will be characterized for a broad class of the initial conditions generated in the course of Keldysh switch-on state. Gradual loss of initial correlations due to interactions and related renormalization processes in the system may, under favorable conditions, give rise to the evolution stage expressible in terms of non-equilibrium quasi-particles.