Abstract:We consider the dynamics of the Bose polaron system, a dense quantum gas consisting of $N$ bosons evolving in $\mathbb{R}^3$ in the presence of an impurity particle. The system is studied in the mean-field scaling with initially high density $\rho$ and large volume $\Lambda$ of the gas. In the initial state, almost all bosons are in the Bose-Einstein condensate, with a few excitations. We derive from the microscopic dynamics, in the joint limit of large densities and volumes, with the constraint $\Lambda^3 \ll \rho$, the effective description by the translation-invariant Bogoliubov-Fröhlich Hamiltonian, which couples the quantum field of excitations linearly to the impurity particle.
| Comments: | Minor corrections and improved presentation |
| Subjects: | Mathematical Physics (math-ph) |
| Cite as: | arXiv:2604.11976 [math-ph] |
| (or arXiv:2604.11976v2 [math-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2604.11976 arXiv-issued DOI via DataCite |
From: Siegfried Spruck [view email]
[v1]
Mon, 13 Apr 2026 19:08:58 UTC (72 KB)
[v2]
Fri, 22 May 2026 15:06:14 UTC (72 KB)
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