Dissipative Two‐State System at Non‐Equilibrium: Real Time Green's Function Approach

In this paper we study the dynamical properties of a dissipative two-state fermionic system embedded in a phonon bath at finite temperature. The non-equilibrium thermo field dynamics, a real time formalism of thermal quantum field theory, is employed to formulate time dependent energy renormalization and derive transport equations. The renormalization procedures derived in this paper replace the on-shell energy definitions in stationary situations and thus can be used in any situations. The procedure reduces to that of equilibrium situations when there is no time dependence. We show that in a system where there are many coupled stages (with multi-components) quantum fluctuations among these states cannot be eliminated so that the long time limit of non-equilibrium theory does not exactly reproduce an equilibrium theory. The procedures and conclusions obtained also apply to more general systems with multi-components.