Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates

TL;DR

This paper rigorously analyzes the vortex distribution in a rotating Bose-Einstein condensate, revealing it to be strongly inhomogeneous near the critical rotation speed and gradually becoming uniform as rotation increases, using advanced mathematical techniques.

Contribution

It provides a rigorous derivation of the inhomogeneous vortex distribution in the strongly interacting regime without relying on compactness arguments.

Findings

Vortex distribution is strongly inhomogeneous near the critical speed.

Vortex distribution gradually homogenizes with increased rotation speed.

Explicit estimates on vorticity measure differences are provided.

Abstract

We consider a 2D rotating Bose gas described by the Gross-Pitaevskii (GP) theory and investigate the properties of the ground state of the theory for rotational speeds close to the critical speed for vortex nucleation. While one could expect that the vortex distribution should be homogeneous within the condensate we prove by means of an asymptotic analysis in the strongly interacting (Thomas-Fermi) regime that it is not. More precisely we rigorously derive a formula due to Sheehy and Radzihovsky [Phys. Rev. A 70, 063620(R) (2004)] for the vortex distribution, a consequence of which is that the vortex distribution is strongly inhomogeneous close to the critical speed and gradually homogenizes when the rotation speed is increased. From the mathematical point of view, a novelty of our approach is that we do not use any compactness argument in the proof, but instead provide explicit estimates on the difference between the vorticity measure of the GP ground state and the minimizer of a certain renormalized energy functional.