Statistical properties of polarons in a magnetic field. I. Analytic results

Abstract

The free energy of an ideal polaron gas in a static magnetic field is calculated using Feynman's path-integral formalism. The trial action, used in Feynman's polaron theory, is extended to take into account the anisotropy of the effective electron-phonon interaction. This results in a free-energy expression with four variational parameters. According to Feynman's conjecture, the resulting free energy is an upper bound to the exact result. The approximate free energy is expected to provide accurate results for arbitrary electron-phonon coupling strength ($\alpha$), temperature ($T$), and magnetic field strength ($\mathcal{H}$). The free energy per polaron is evaluated for limiting values of $\alpha$, $T$, and $\mathcal{H}$.