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

Abstract : 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.
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Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-03035282
Contributor : Jonas Lampart <>
Submitted on : Friday, July 9, 2021 - 9:53:48 AM
Last modification on : Tuesday, July 13, 2021 - 3:38:13 AM

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Lampart, Pickl - Tracer Bogoli...
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### Identifiers

• HAL Id : hal-03035282, version 2
• ARXIV : 2011.14428

### Citation

Jonas Lampart, Peter Pickl. Dynamics of a tracer particle interacting with excitations of a Bose-Einstein condensate. 2021. ⟨hal-03035282v2⟩

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