# Self-adjointness and domain of the Fröhlich Hamiltonian

@article{Griesemer2015SelfadjointnessAD, title={Self-adjointness and domain of the Fr{\"o}hlich Hamiltonian}, author={Marcel Griesemer and Adolf Wuensch}, journal={Journal of Mathematical Physics}, year={2015}, volume={57}, pages={021902} }

In the large polaron model of Herbert Frohlich, 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 Frohlich 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…

## 31 Citations

Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron

- Physics, MathematicsCommunications on Pure and Applied Mathematics
- 2020

We consider the Fröhlich polaron model in the strong coupling limit. It is well‐known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we…

Microscopic Derivation of Time-dependent Point Interactions

- Physics, Mathematics
- 2019

We study the dynamics of the three-dimensional Frohlich polaron -- a quantum particle coupled to a bosonic field -- in the quasi-classical regime, i.e., when the field is very intense and the…

Effective Potentials Generated by Field Interaction in the Quasi-Classical Limit

- Mathematics, Physics
- 2017

We study the quasi-classical limit of a quantum system composed of finitely many nonrelativistic particles coupled to a quantized field in Nelson-type models. We prove that, as the field becomes…

On the dynamics of polarons in the strong-coupling limit

- Physics, Mathematics
- 2016

The polaron model of H. Frohlich describes an electron coupled to the quantized longitudinal optical modes of a polar crystal. In the strong-coupling limit, one expects that the phonon modes may be…

Direct integral description of angulon

- Mathematics
- 2016

We propose a representation of angulon in which the angulon operator is decomposable relative to the field of Hilbert spaces over the probability measure space, and the probability measure…

The renormalized Bogoliubov–Fröhlich Hamiltonian

- PhysicsJournal of Mathematical Physics
- 2020

The Bogoliubov–Frohlich Hamiltonian models the interaction of an impurity with the excitations of a Bose–Einstein condensate. It has been observed that the dependence of the ground state energy on…

Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

- PhysicsArchive for rational mechanics and analysis
- 2021

The Fröhlich Hamiltonian is considered in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field and it is shown that the dynamics of the system is approximately described by the Landau–Pekar equations.

A note on the Fr\"ohlich dynamics in the strong coupling limit

- Physics
- 2020

We revise a previous result about the Fröhlich dynamics in the strong coupling limit obtained in [Gri17]. In the latter it was shown that the Fröhlich time evolution applied to the initial state φ0 ⊗…

Effective Mass of the Polaron—Revisited

- Mathematics, PhysicsAnnales Henri Poincaré
- 2020

Properties of the energy–momentum relation for the Fröhlich polaron are of continuing interest, especially for large values of the coupling constant. By combining spectral theory with the available…

Hamiltonians for polaron models with subcritical ultraviolet singularities

- Physics
- 2022

We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity,…

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