Electron tunneling dynamics in anharmonic bath

Tunneling transition probability for a particle interacting with an anharmonic bath is found in a time-dependent Hartree approximation. The general expression is presented in terms of medium Keldysh functions that are assumed to be known. Furthermore, the transition probability is calculated in the noninteracting-blip approximation where the rate constant does not exhibit an activation dependence at high temperatures. The reorganization energy $Er$ and the renormalized reaction heat $ε̃$ are experessed in terms of the correlation matrix for a solvent and internal modes in both quantum and classical regimes. It is shown that $Er$ and $ε̃$ are temperature dependent.