Polaron density matrix and effective mass at finite temperature

Abstract

We calculate the density matrix elements of the polaron using Feynman's variational method. The density matrix is diagonalized, and the eigenvalues and eigenfunctions are derived. These results and the calculated density matrix are used to evaluate the root-mean-square (rms) displacements ${R}_{\ensuremath{\beta}}$ and the effective mass (EM) ${m}^{*}$ for various values of coupling strengths between electron and medium and of the temperature. We find that EM is related to the rms displacement. The temperature dependence of the EM is in qualitative agreement with experiment.