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

Abstract

AbstractWe study the Fröhlich polaron model in $\mathbf {R}^{3}$ 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 $\alpha ^{4}$ α 4 for large coupling constant $\alpha $ α .