Path integral approach to polaron mass and radius at finite temperatures

Polaron effective mass and radius at finite temperatures are defined and exact path integral representations are given for them. Feynman's representation for the effective mass is obtained in the limit of zero temperature. Calculations are made in the framework of the variational principle for the free energy by using as trial functional the one corresponding to a simplified, exactly solvable model of electron-phonon interaction proposed by Bogolubov. Effective mass and radius dependence on temperature and coupling strength are discussed for some ranges of values of these parameters. Comparison with the experimental dependence of polaron cyclotron mass on temperature shows a reasonable agreement.