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

Abstract

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.

61 pages, 1 figure

References in corpus (6)

• Effective mass of the Polaron: a lower bound
• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• On the global minimum of the energy-momentum relation for the polaron
• Upper and lower bounds for the large polaron dispersion in $D=1,2,3$ dimensions
• The effective mass problem for the Landau-Pekar equations
• Polaron models with regular interactions at strong coupling

Cited by in corpus (5)

• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• On the global minimum of the energy-momentum relation for the polaron
• Ubiquity of bound states for the strongly coupled polaron
• The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass
• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling