Bogoliubov Spectrum of Interacting Bose Gases

@article{Lewin2012BogoliubovSO,
  title={Bogoliubov Spectrum of Interacting Bose Gases},
  author={Mathieu Lewin and Phan Th{\`a}nh Nam and Sylvia Serfaty and Jan Philip Solovej},
  journal={Communications on Pure and Applied Mathematics},
  year={2012},
  volume={68}
}
We study the large‐N limit of a system of N bosons interacting with a potential of intensity 1/N. When the ground state energy is to the first order given by Hartree's theory, we study the next order, predicted by Bogoliubov's theory. We show the convergence of the lower eigenvalues and eigenfunctions towards that of the Bogoliubov Hamiltonian (up to a convenient unitary transform). We also prove the convergence of the free energy when the system is sufficiently trapped. Our results are valid… 
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