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

2022/11/07 by Morris Brooks, Robert Seiringer, Brooks, Morris +1 · 3 citations
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2211.03353

Abstract

We study the Fröhlich polaron model in ℝ³, 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 α⁴ for large coupling constant α.

Cited by

• Semiclassical limit of polaron dynamics with cutoff
• Wigner measure approach to the derivation of the Landau-Pekar equations in the mean-field limit
• Convergence of states for polaron models in the classical limit

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