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The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass
Publications Mathématiques de l'IHÉS, Volume 140 (2024), pp. 271-309
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We study the Fröhlich polaron model in 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 α 4 for large coupling constant α.

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DOI: 10.1007/s10240-024-00150-0

Morris Brooks 1; Robert Seiringer 1

1 
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Morris Brooks; Robert Seiringer. The Fröhlich polaron at strong coupling: Part II — Energy-momentum relation and effective mass. Publications Mathématiques de l'IHÉS, Volume 140 (2024), pp. 271-309. doi: 10.1007/s10240-024-00150-0

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