T. Isoshima et K. Machida, EXCITATION SPECTRUM IN A CYLINDRICAL BOSE-EINSTEIN CONDENSATE, Journal of the Physical Society of Japan, 67(6), 1998, pp. 1840-1843
The entire excitation spectrum within the Popov approximation of the B
ogoliubov theory for a cylindrically symmetric Bose-Einstein condensat
e radially trapped by a harmonic potential is calculated. The full dis
persion relation and the temperature dependence of its zero sound mode
propagating along the axial direction are evaluated in a self-consist
ent 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.