An analysis of electronic dephasing in the spin-boson model

In order to develop a more complete understanding of the limitations of mixed quantum-classical simulation methods, the origins of electronic dephasing are analyzed in a simple model of the condensed phase, namely, the spin-boson model with an ohmic spectral density. We focus on the decay of the thermally averaged nuclear overlap/phase function (NOPF). Considering the strong coupling/high temperature limit, a relationship is obtained at short time between the rate of electronic coherence loss and the electronic dephasing rate characteristic of a classical bath. Using this relationship, we clarify the origin of the decay of the NOPF. In the same limit, we also reproduce an earlier relationship between the electronic decoherence time and a solvation relaxation time. Finally, we point out that, for the spin-boson model, the exact quantum mechanical description of electronic dephasing is reproduced by mixed quantum/classical methods if a Gaussian distribution of quantum fluctuations around each classical phase space point is introduced. That spatial distribution of quantum fluctuations is functionally the same as that appearing in the Feynman-Kleinert variational local harmonic approximation, and also that implemented in existing classical trajectory-based estimates of coherence dissipation times.