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

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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 Fröhlich polaron and the low-temperature polaron mobility (which was under a long-time debate) is found with a correction due to initial correlations.