Evolution of a subsystem in a heat bath with no initial factorized state assumption

A problem of the realistic initial conditions for the evolution equation of the statistical operator of a subsystem in interaction with a heat bath is addressed. Starting from the canonical equilibrium distribution for a full subsystem-heat bath system, the evolution of a subsystem driven by an external force is considered. The exact new homogeneous time-convolution and time-convolutionless (time-local) generalized master equations for a subsystem statistical operator are obtained. They include initial (conventionally ignored) correlations on an equal footing with collisions in the kernel governing their evolution. No conventional initial factorized state assumption is used. In the  second-order approximation on the subsystem-heat bath interaction, when both equations become identical, time-local and essentially simpler, they are applied to the electron-phonon system in an external electric field. It is shown, that, in general, the initial correlations influence the subsystem's evolution in time. It is also explicitly demonstrated (in the linear response regime), that on the large timescale (actually at t→∞) initial correlations cease to influence the electron evolution in time, the time-reversal symmetry breaks and the subsystem enters the kinetic irreversible regime. At the same time, the initial correlations contribute to kinetic coefficients like the electron mobility. As an application, the low-temperature mobility for weak coupling (Fröhlich) polaron and arbitrary coupling (Feynman) polaron, which was under debate for a long time, is obtained. It shows the corrections to polaron mobility due to initial correlations.