Geodesic
Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
Forum of Mathematics, Sigma, Tome 11 (2023)

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We consider the large polaron described by the Fröhlich Hamiltonian and study its energy-momentum relation defined as the lowest possible energy as a function of the total momentum. Using a suitable family of trial states, we derive an optimal parabolic upper bound for the energy-momentum relation in the limit of strong coupling. The upper bound consists of a momentum independent term that agrees with the predicted two-term expansion for the ground state energy of the strongly coupled polaron at rest and a term that is quadratic in the momentum with coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar. 
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David Mitrouskas; Krzysztof Myśliwy; Robert Seiringer. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.45

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