Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate

Formation of stationary three-dimensional (3D) wave patterns generated by a small pointlike impurity moving through a Bose-Einstein condensate with supersonic velocity is studied. Asymptotic formulae for a stationary far-field density distribution are obtained. Comparison with the three-dimensional numerical simulations demonstrates that these formulae are accurate enough already at the distances from the obstacle equal to a few wavelengths.

Figure 1

Coordinates defining the radius vector $\mathbf{r}$ and the wave vector $\mathbf{k}$. The latter is normal to the wave crest line of the ship wave which is shown schematically by a curve.

Figure 2

(Color online) Numerically simulated wave pattern generated by a spherical obstacle moving through a Bose-Einstein condensate. The parameters of the BEC are indicated in the text. The analytical wave crest lines are shown by dashed lines. These are plotted according to Eq. (22).

Figure 3

(Color online) Oscillatory structure in front of the obstacle obtained by numerical simulations (solid line) and analytically [Eq. (30)]; dashed line). Position of the obstacle is shown by a dot.