Influence of initial correlations on evolution of correlation function of a subsystem interacting with a quantum field (heat bath) and polaron mobility

TL;DR

This paper develops an exact approach to account for initial correlations in the evolution of correlation functions of a subsystem interacting with a quantum field, demonstrating their influence on dynamics and applying it to polaron mobility.

Contribution

It introduces a new exact homogeneous equation for correlation functions that incorporates initial correlations without conventional approximations, advancing the understanding of subsystem dynamics.

Findings

Initial correlations affect the correlation function's evolution over time.

The influence of initial correlations diminishes on large timescales.

Applied to the Fröhlich polaron, the approach yields a corrected low-temperature mobility.

Abstract

A regular approach to accounting for initial correlations, which allows to go beyond the unrealistic random phase (initial product state) approximation in deriving the evolution equations, is suggested. An exact homogeneous equation for a two-time equilibrium correlation function for the dynamical variables of a subsystem interacting with a boson field (heat bath) is obtained. No conventional approximation like RPA or Bogoliubov's principle of weakening of initial correlations is used. The obtained equation takes into account the initial correlations in the kernel governing its evolution. The solution to this equation is found in the second order of the kernel expansion in the electron-phonon interaction, which demonstrates that generally the initial correlations influence the correlation function's evolution in time. It is shown that this influence vanishes on a large timescale. The developed approach is applied to the Fr\"ohlich polaron and the low-temperature polaron mobility (which was under a long-time debate) is found with a correction due to initial correlations.