Manifestation of superfluidity in an evolving Bose-condensed gas

We study the generation of excitations due to an ''impurity''(static perturbation) placed into an oscillating Bose-condensed gas in the time-dependent trapping field. It is shown that there are two regions for the position of the local perturbation. In the first region the condensate flows around the ''impurity'' without generation of excitations demonstrating superfluid properties. In the second region the creation of excitations occurs, at least within a limited time interval, revealing destruction of superfluidity. The phenomenon can be studied by measuring the damping of condensate oscillations at different positions of the ''impurity''.