You are currently offline. Some features of the site may not work correctly.

Corpus ID: 235592804

Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime

@inproceedings{Nam2021BogoliubovES,
title={Bogoliubov excitation spectrum of trapped Bose gases in the Gross-Pitaevskii regime},
author={Phan Th{\`a}nh Nam and Arnaud Triay},
year={2021}
}

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.

We consider systems ofN bosons in R, trapped by an external potential. The interaction is repulsive and has a scattering length of the order N (Gross-Pitaevskii regime). We determine the ground state… Expand

We study a system of N trapped bosons in the Thomas-Fermi regime with an interacting pair potential of the form gNN V pNxq, for some β P p0, 1{3q and gN diverging as N Ñ 8. We prove that there is… Expand

We verify Bogoliubov’s approximation for translation invariant Bose gases in the mean field regime, i.e. we prove that the ground state energy EN is given by EN = NeH+inf σ (H)+oN→∞(1), whereN is the… Expand