Bogoliubov excitation spectrum of trapped Bose gases in the GrossPitaevskii 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 $N^2 V(N(xy))$. We prove that the lowenergy excitation spectrum of the system is determined by the eigenvalues of an effective oneparticle operator, which agrees with Bogoliubov's approximation.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.11949
 Bibcode:
 2021arXiv210611949T
 Keywords:

 Mathematical Physics
 EPrint:
 68 pages