The internal structure of a vortex and its exited states in a two dimensional superfluid

The motion of quantum vortex in a two-dimensional spinless superfluid is analyzed within Popov's hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov's action, which allow for weak solutions of the Gross-Pitaevskii equation. The resulting equations are solved for a vortex moving with respect to the superfluid. It is  found that the vortex core is reconstructed in a non-analytic way. The response of the vortex to applied force produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.