The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass

Abstract

We study the Fröhlich polaron model in \(\mathbf {R}^{3}\), and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In combination with a corresponding upper bound proved earlier (Mitrouskas et al. in Forum Math. Sigma 11:1–52, 2023), it shows that the energy is approximately parabolic below the continuum threshold, and that the polaron’s effective mass (defined as the semi-latus rectum of the parabola) is given by the celebrated Landau–Pekar formula. In particular, it diverges as \(\alpha ^{4}\) for large coupling constant \(\alpha \).