• Corpus ID: 235592804

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

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