Excitation spectrum in a cylindrical Bose-Einstein condensate

The entire excitation spectrum within the Popov approximation of the Bogoliubov theory for a cylindrically symmetric Bose-Einstein condensate radially trapped by a harmonic potential is calculated. The full dispersion relation and the temperature dependence of its zero sound mode propagating along the axial direction are evaluated in a self-consistent manner. The sound velocity is shown to depend not only on the peak density, hut also on the axial area density. Recently conducted sound velocity experiment on a gas of Na atoms is discussed in light of the present theory.