Polaron Mobility at Finite Temperature

The Kadanoff-Baym transport theory leads to an expression for polaron mobility which becomes exact for low, but finite, temperature, $e^{\frac{\Theta }{T}}\gg 1$, but not necessarily $\frac{\Theta }{T}\gg 1$. This expression is evaluated exactly in the weak-coupling limit. Comparison with previous variational calculations shows that the latter have not predicted even qualitatively valid corrections to the known asymptotic zero-temperature result. Simple arguments allow the present weak-coupling expression to be extended to finite coupling. These arguments are verified by a quantitative calculation using the Feynman model. It is found that the corrections due to finite temperature are at least as important as those due to a finite coupling constant.