Bogoliubov Spectrum of Interacting Bose Gases

摘要: We study the large-N limit of a system N bosons interacting with potential intensity 1/N. When ground state energy is to first order given by Hartree's theory, we next order, predicted Bogoliubov's theory. show convergence lower eigenvalues and eigenfunctions towards that Bogoliubov Hamiltonian (up convenient unitary transform). also prove free when sufficiently trapped. Our results are valid in an abstract setting, our main assumptions being Hartree unique non-degenerate, there complete Bose-Einstein condensation on this state. Using method then treat two applications: atoms ''bosonic'' electrons one hand, trapped 2D 3D Coulomb gases other hand.