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arXiv · 2107.05195

Tracer particles coupled to an interacting boson gas

Esteban Cárdenas
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Abstract

In this work, we investigate the mean-field limit of a model consisting in $m \geq 1 $ tracer particles, coupled to an interacting boson field. We assume the mass of the tracer particles and the expected number of bosons to be of the same order of magnitude $N \geq 1 $ and we investigate the $N\rightarrow \infty $ limit. In particular, we show that the limiting system can be effectively described by a pair of variables $( \textbf{X}_t ,φ_t ) \in \mathbb{R}^{3m} \times H^1(\mathbb{R}^3)$ that solve a mean-field equation. Our methods are based on proving estimates for the number of bosonic particles in a suitable \textit{fluctuation state} $Ω_{N,t }$. The main diffculty of the problem comes from the fact that the interaction with the tracer particles can create or destroy bosons for states close to the vacuum.

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Esteban Cárdenas. 2021-08-16. Tracer particles coupled to an interacting boson gas. https://arxiv.org/abs/2107.05195

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