On the global minimum of the energy-momentum relation for the polaron

Abstract

For the Fröhlich model of the large polaron, we prove that the ground state energy as a function of the total momentum has a unique global minimum at momentum zero. This implies the non-existence of a ground state of the Fröhlich Hamiltonian and thus excludes the possibility of a localization transition at finite coupling.

14 pages

References in corpus (4)

• Effective mass of the Polaron: a lower bound
• The Fröhlich Polaron at Strong Coupling -- Part I: The Quantum Correction to the Classical Energy
• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• The resolvent of the Nelson Hamiltonian improves positivity

Cited by in corpus (5)

• Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron
• Ubiquity of bound states for the strongly coupled polaron
• The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass
• Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling
• Asymptotic series for low-energy excitations of the Fröhlich Polaron at strong coupling