The excitation spectrum for weakly interacting bosons in a trap
  We investigate the low-energy excitation spectrum of a Bose gas confined in a trap, with weak long-range repulsive interactions. In particular, we prove that the spectrum can be described in terms of the eigenvalues of an effective one-particle operator, as predicted by the Bogoliubov approximation. 
Philip Grech, Robert Seiringer
math-ph cond-mat.quant-gas math.MP math.SP