Microscopic derivation of the Fröhlich Hamiltonian for the Bose polaron in the mean-field limit

Abstract

We consider the quantum mechanical many-body problem of a single impurity particle immersed in a weakly interacting Bose gas. The impurity interacts with the bosons via a two-body potential. We study the Hamiltonian of this system in the mean-field limit and rigorously show that, at low energies, the problem is well described by the Fröhlich polaron model.

LaTeX, 20 pages, final version to appear in Annales Henri Poincare

References in corpus (5)

• Rotation of quantum impurities in the presence of a many-body environment
• The Second Order Upper Bound for the Ground Energy of a Bose Gas
• The ground state energy of a low density Bose gas: a second order upper bound
• The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions
• Introduction to polaron physics: Basic Concepts and Models

Cited by in corpus (6)

• Quantum dynamics of Bose-polaron in a $d$-dimensional Bose Einstein condensate
• Quench Dynamics of the Ideal Bose Polaron at Zero and Nonzero Temperatures
• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime
• A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate
• Validity of the Fröhlich model for a mobile impurity in a Bose-Einstein condensate
• Effective Polaron Dynamics of an Impurity Particle Interacting with a Fermi Gas