Dynamics of a tracer particle interacting with excitations of a Bose-Einstein condensate

Jonas Lampart (1, 2) , Peter Pickl

1 ICB - Laboratoire Interdisciplinaire Carnot de Bourgogne
2 CNRS - Centre National de la Recherche Scientifique

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 essentially form a homogeneous Bose-Einstein condensate, with some excitations. With an appropriate mean-field scaling of the interactions, we prove that the effective dynamics for $N\to \infty$ is generated by the Bogoliubov-Fr\"ohlich Hamiltonian, which couples the tracer particle linearly to the excitation field.

Domaines: Physique mathématique [math-ph]

Jonas Lampart, Peter Pickl. Dynamics of a tracer particle interacting with excitations of a Bose-Einstein condensate. 2020. ⟨hal-03035282v1⟩