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arXiv · 1801.06850

Mean field dynamics of a quantum tracer particle interacting with a boson gas

Thomas Chen·Avy Soffer
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Abstract

We consider the dynamics of a heavy quantum tracer particle coupled to a non-relativistic boson field in ${\mathbb R}^3$. The pair interactions of the bosons are of mean-field type, with coupling strength proportional to $\frac1N$ where $N$ is the expected particle number. Assuming that the mass of the tracer particle is proportional to $N$, we derive generalized Hartree equations in the limit $N\rightarrow\infty$. Moreover, we prove the global well-posedness of the associated Cauchy problem for sufficiently weak interaction potentials.

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Thomas Chen, Avy Soffer. 2018-01-21. Mean field dynamics of a quantum tracer particle interacting with a boson gas. https://arxiv.org/abs/1801.06850

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