The Internal Structure of Vortices in Bosonic Superfluids and its Implications

The standard theory of bosonic superfluids assumes that vortices are analogous to monopole point charges, and are therefore characterized by quantum numbers that describe only their position and (vorticity) charge. This textbook description is derived from a cornerstone of fluid mechanics -- the Kelvin theorem -- which invokes the conservation of circulation in the dynamics of ideal incompressible fluids. However, in this talk I will show that in a broad class of superfluids, vortices are characterized by an additional degree of freedom, affecting significantly various physical phenomena. This new degree of freedom, which endows to vortices a dipole-like nature, stems from a non-analytic "core reconstruction" which takes place in superfluids with a large healing length, yielding a set of excited states of the vortex state with low energies and long lifetime. From a mathematical perspective, these new solutions of the Gross-Pitaevskii equations are “weak solutions”. Namely, they minimize the action but do not satisfy the corresponding variational equations over a set of zero measure. The consequences of the non-analytic core reconstruction regarding the transport properties of velocities in disorder media and the instability of Abrikosov’s lattice will be presented.