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
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References
SHOWING 1-10 OF 13 REFERENCES
Interaction of Nonrelativistic Particles with a Quantized Scalar Field
- Physics, Mathematics
- 1964
We demonstrate the mathematical existence of a meson theory with nonrelativistic nucleons. A system of Schrodinger particles is coupled to a quantized relativistic scalar field. If a cutoff is put on…
Dynamics of a Strongly Coupled Polaron
- Physics
- 2014
We study the dynamics of large polarons described by the Fröhlich Hamiltonian in the limit of strong coupling. The initial conditions are (perturbations of) product states of an electron wave…
Spectral properties of an optical polaron in a magnetic field
- Physics
- 1988
An optical polaron, which is exposed to a homogeneous magnetic field, is considered. Making use of functional analytical methods of Frohlich [Fortschr. Phys. 22, 159 (1974)], it is proved that the…
XX. Properties of slow electrons in polar materials
- Physics
- 1950
Summary Using a variational method we have investigated the properties of the lowest energy levels in a range ħω above the ground level of the system consisting of an electron and a continuous…
Asymptotic Completeness for a Renormalized Nonrelativistic Hamiltonian in Quantum Field Theory: The Nelson Model
- Mathematics
- 2000
Scattering theory for the Nelson model is studied. We show Rosen estimates and we prove the existence of a ground state for the Nelson Hamiltonian. Also we prove that it has a locally finite pure…
Unbounded Self-adjoint Operators on Hilbert Space
- Mathematics
- 2012
I Basics onClosed Operators.- 1 Closed Operators and Adjoint Operators.- 2 Spectrum of Closed Operators.- 3 Some Classes of Unbounded Operators.- II Spectral Theory.- 4 Spectral Measures and Spectral…
Existence of Dressed One Electron States in a Class of Persistent Models
- Physics
- 1974
In this paper the dynamics of a class of simple models (so called persistent models) including Nelson's model is studied. These models describe conserved, non relativistic, scalar electrons…