# 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} }

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.

## 11 Citations

Microscopic Derivation of the Fröhlich Hamiltonian for the Bose Polaron in the Mean-Field Limit

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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

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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…

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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…

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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…

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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

- Physics
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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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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.

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- PhysicsSymmetry
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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

- PhysicsSpringer INdAM Series
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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…

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