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

We consider the large polaron described by the Frohlich 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.

Automated summary

We study the energy-momentum relation of a large polaron described by the Frohlich Hamiltonian. By 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. This upper bound consists of a momentum independent term matching the predicted two-term expansion of the ground state energy for the strongly coupled polaron at rest, and a term quadratic in momentum with a coefficient given by the inverse of twice the classical effective mass introduced by Landau and Pekar.