Collective excitations of trapped Fermi or Bose gases

Abstract

A new method is developed to calculate all excitations of trapped gases using hydrodynamics at zero temperature for any equation of state $\mu =\mu (n)$ and for any trapping potential. It is shown that a natural scalar product can be defined for the mode functions, by which the wave operator is hermitian and the mode functions are orthogonal. It is also shown that the Kohn-modes are exact for harmonic trapping in hydrodynamic theory. Excitations for fermions are calculated in the BCS-BEC transition region using the equation of state of the mean-field Leggett-model for isotrop harmonic trap potential.

4 pages, 3 figures