Self-Adjointness and Domain of the Froehlich Hamiltonian

Abstract

In the large polaron model of H. Froehlich, the electron-phonon interaction is a small perturbation in form sense, but a large perturbation in operator sense. This means that the form-domain of the Hamiltonian is not affected by the interaction but the domain of self-adjointness is. In the particular case of the Froehlich model, we are nevertheless able, thanks to a recently published new operator bound, to give an explicit characterization of the domain in terms of a suitable dressing transform. Using the mapping properties of this dressing transform, we analyze the smoothness of vectors in the domain of the Hamiltonian with respect to the position of the electron.

20 pages, with some clarifications and improvements compared to version 1. To appear in Journal of Mathematical Physics

References in corpus (1)

• Dynamics of a strongly coupled polaron

Cited by in corpus (26)

• On Nelson-type Hamiltonians and abstract boundary conditions
• On the domain of the Nelson Hamiltonian
• Particle Creation at a Point Source by Means of Interior-Boundary Conditions
• On the dynamics of polarons in the strong-coupling limit
• Quantum corrections to the Pekar asymptotics of a strongly coupled polaron
• Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit
• The Renormalised Bogoliubov-Fröhlich Hamiltonian
• Divergence of the effective mass of a polaron in the strong coupling limit
• On a Direct Description of Pseudorelativistic Nelson Hamiltonians
• Effective mass of the polaron -- revisited
• The Polaron at Strong Coupling
• Derivation of the Landau-Pekar equations in a many-body mean-field limit
• Quasi-Classical Dynamics
• A note on the Fröhlich dynamics in the strong coupling limit
• Self-adjointness of a class of multi-spin-boson models with ultraviolet divergences
• On the global minimum of the energy-momentum relation for the polaron
• Microscopic Derivation of Time-dependent Point Interactions
• Hamiltonians for polaron models with subcritical ultraviolet singularities
• Ubiquity of bound states for the strongly coupled polaron
• The Strongly Coupled Polaron on the Torus: Quantum Corrections to the Pekar Asymptotics
• Extended State Space for describing renormalized Fock spaces in QFT
• Absence of excited eigenvalues for Fröhlich type polaron models at weak coupling
• The Lieb--Thomas strategy for strongly coupled fermionic multipolarons with general external fields
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• A model for reducing the angulon operator
• Direct integral description of angulon