Theory of Polaron Mobility

Abstract

The polaron mobility is calculated by making use of the general theory of electrical conductivity. We take the states determined by Feynman's trial action as the unperturbed states and treat the difference between the true action and the trial action as a perturbation. Numerical values of the polaron mobility at very .low temperatures are given and are dis· cussed in comparison with the results obtained by Shultz and .by Morita. § I. Introduction We have investigated the static properties of polaron at finite temperatures in the previous paper 1 > (hereafter referred to as I). We shall investigB;te the polaron mobility in the present paper. In the same way as in I, we calculate the polaron mobility by using Feynman's path-integral method. In the polaron problem, the interaction between an electron and lattice vibrations is so large that the usual perturbation theoretic treatment fails. Therefore the calculation of the mobility in the present paper will be based on the general theory of electrical conductivity recently developed by many authors, 2 > which is applicable to a system which does not allow us to set up the Boltzmann equation. We take the states determined by Feynman's trial action as unperturbed states and treat the difference between the trial action and the true action as a perturbation which yields a decay of electronic current correlation. The following assumptions will be made in the present paper. i) The electrical conductivity is determined by the asymptotic form of a correlation function of electronic current. ii) This asymptotic form has the property of exponential decay in time. These assumptions are valid in the case of weak interaction. It is not sure whether or not they are applicable to the present problem which includes the case of strong interaction. In the present treatment , however, ~he states determined by Feynman's trial action instead of the states of a free electron are chosen as the unperturbed states. It is expected that the perturbation in the former case may be made weaker than in the latter case and that the above mentioned assumptions may be valid. In fact the self-energy of polaron at 0°K calculated by using these assumptions agrees with that obtained by Feynman 3 > as will be shown _in § 3. Therefore, the approxi