The renormalized Bogoliubov–Fröhlich Hamiltonian

@article{Lampart2020TheRB,
  title={The renormalized Bogoliubov–Fr{\"o}hlich Hamiltonian},
  author={Jonas Lampart},
  journal={Journal of Mathematical Physics},
  year={2020}
}
  • J. Lampart
  • Published 5 September 2019
  • Physics
  • Journal of Mathematical Physics
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 the ultraviolet (UV) cutoff differs significantly from what would be expected from similar well-known models. We give a detailed explanation of this UV behavior and provide an explicit representation of the renormalized Hamiltonian. 
Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit
We consider the quantum mechanical many-body problem of a single particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the
The Resolvent of the Nelson Hamiltonian Improves Positivity
We give a new proof that the resolvent of the renormalised Nelson Hamiltonian at fixed total momentum P improves positivity in the (momentum) Fock-representation, for every P . The argument is based
Dynamics of a tracer particle interacting with excitations of a Bose-Einstein condensate
We consider the quantum dynamics of a large number $N$ of interacting bosons coupled a tracer particle, i.e. a particle of another kind, on a torus. We assume that in the initial state the bosons
An abstract framework for interior-boundary conditions
In a configuration space whose boundary can be identified with a subset of its interior, a boundary condition can relate the behaviour of a function on the boundary and in the interior. Additionally,
On the Self-Adjointness of H+A∗+A
Let $H:D(H)\subseteq{\mathscr F}\to{\mathscr F}$ be self-adjoint and let $A:D(H)\to{\mathscr F}$ (playing the role of the annihilator operator) be $H$-bounded. Assuming some additional hypotheses on
General memory kernels and further corrections to the variational path integral approach for the Bogoliubov-Fröhlich Hamiltonian
The celebrated variational path integral approach to the polaron problem shows remarkable discrepancies with diagrammatic Monte Carlo for the Bogoliubov-Fr¨ohlich Hamiltonian which describes an
Hamiltonians for polaron models with subcritical ultraviolet singularities
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,
On the Ultraviolet Limit of the Pauli–Fierz Hamiltonian in the Lieb–Loss Model
TLDR
The ground state energy of a free, nonrelativistic electron coupled to the quantized radiation field by the infimum is approximated by the jats:inline-formula.
Boundary Conditions that Remove Certain Ultraviolet Divergences
TLDR
A novel way of removing UV divergences is reviewed: by imposing a type of boundary condition on the wave function that allows for a direct definition of the Hamiltonian without renormalization or limiting procedures.
Ultraviolet Properties of a Polaron Model with Point Interactions and a Number Cutoff
A BSTRACT . We discuss a model in which a nonrelativistic particle can absorb and emit bosonic particles on contact. The bosons have a constant dispersion relation, as in the related Fröhlich polaron
...
...

References

SHOWING 1-10 OF 48 REFERENCES
Feynman path-integral treatment of the Bose polaron beyond the Fröhlich model
An impurity immersed in a Bose-Einstein condensate is no longer accurately described by the Frohlich Hamiltonian as the coupling between the impurity and the boson bath gets stronger. We study the
All-coupling theory for the Fröhlich polaron
The Fr\"ohlich model describes the interaction of a mobile impurity with a surrounding bath of phonons which leads to the formation of a quasiparticle, the polaron. In this paper an efficient
Self-adjointness and domain of the Fröhlich Hamiltonian
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
On Nelson-Type Hamiltonians and Abstract Boundary Conditions
We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation
Van Hove Hamiltonians – Exactly Solvable Models of the Infrared and Ultraviolet Problem
Abstract. Quadratic bosonic Hamiltonians with a linear perturbation are studied. Depending on the infrared and ultraviolet behavior of the perturbation, their properties are described from the point
Interaction of Nonrelativistic Particles with a Quantized Scalar Field
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
Quantum Dynamics of Ultracold Bose Polarons.
TLDR
A surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes.
Strong coupling treatment of the polaronic system consisting of an impurity in a condensate
The strong coupling treatment of the Fröhlich-type polaronic system, based on a canonical transformation and a standard Landau-Pekar type variational wave function, is applied to the polaronic system
Impurity in a Bose-Einstein Condensate and the Efimov Effect.
TLDR
It is shown that the energy and quasiparticle residue of the dressed impurity (polaron) are significantly lowered by three-body correlations, even for weak interactions where there is no Efimov trimer state in a vacuum.
Quantum dynamics of impurities in a one-dimensional Bose gas
Using a species-selective dipole potential, we create initially localized impurities and investigate their interactions with a majority species of bosonic atoms in a one-dimensional configuration
...
...