Phenomenological damping in trapped atomic Bose-Einstein condensates

The method of phenomenological damping developed by Pitaevskii (Zh. Eksp. Teor. Fiz. 35, 408 (1958) [Sov. Phys. JETP 35, 282 (1959)]) for superfluidity near the $\lambda$ point is simulated numerically for the case of a dilute, alkali, inhomogeneous Bose-condensed gas near absolute zero. We study several features of this method in describing the damping of excitations in a Bose-Einstein condensate. In addition, we show that the method may be employed to obtain numerically accurate ground states for a variety of trap potentials.