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arXiv · 2203.02454

Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron

David Mitrouskas·Krzysztof Myśliwy·Robert Seiringer
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Abstract

We consider the large polaron described by the Fr\"ohlich 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. 2022-03-04. Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron. https://doi.org/10.1017/fms.2023.45

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