The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass

Abstract

We study the Fröhlich polaron model in ${\mathbb{R}}^3$, 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, 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 $\alpha$.

References in corpus (4)

• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• On the global minimum of the energy-momentum relation for the polaron
• The effective mass problem for the Landau-Pekar equations

Cited by in corpus (1)

• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling