Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime
Abstract
We consider an inhomogeneous system of $N$ bosons in $\mathbb{R}^3$ confined by an external potential and interacting via a repulsive potential of the form $N^2 V(N(x-y))$. We prove that the low-energy excitation spectrum of the system is determined by the eigenvalues of an effective one-particle operator, which agrees with Bogoliubov's approximation.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2021
- DOI:
- 10.48550/arXiv.2106.11949
- arXiv:
- arXiv:2106.11949
- Bibcode:
- 2021arXiv210611949T
- Keywords:
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- Mathematical Physics
- E-Print:
- 70 pages, final version, to appear in J. Math. Pures Appl