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.

arXiv comment14 pages

References in corpus (9)

• Erratum: Exact Ground State Energy of the Strong-Coupling Polaron
• Self-Adjointness and Domain of the Froehlich Hamiltonian
• On Nelson-type Hamiltonians and abstract boundary conditions
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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