The Renormalised Bogoliubov-Fr\"ohlich Hamiltonian
Jonas Lampart (LICB, CNRS)
TL;DR
This paper analyzes the ultraviolet cutoff dependence in the Bogoliubov-Fr"ohlich Hamiltonian for impurities in Bose-Einstein condensates, providing a detailed explanation and an explicit renormalized Hamiltonian representation.
Contribution
It offers the first detailed explanation of the UV behavior and introduces an explicit form of the renormalized Hamiltonian for this model.
Findings
UV dependence differs from similar models
Provides an explicit renormalized Hamiltonian
Clarifies the ground state energy behavior
Abstract
The Bogoliubov-Fr\"ohlich 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 cutoff differs significantly from what would be expected from similar well-known models. We give a detailed explanation of this UV behaviour, and provide an explicit representation of the renormalised Hamiltonian.
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