Rapidly Rotating Bose-Einstein Condensates in Homogeneous Traps

TL;DR

This paper rigorously analyzes the asymptotic behavior of the ground state energy and density profile of rapidly rotating Bose-Einstein condensates in two-dimensional homogeneous traps with potentials of the form V(r) = r^s, as the coupling constant becomes large and rotation speed increases.

Contribution

It extends previous results to a broader class of confining potentials V(r) = r^s, deriving the leading asymptotics in the high rotation and strong coupling limit.

Findings

Derived the leading asymptotics of the ground state energy.

Determined the density profile in the high rotation limit.

Discussed the case of asymptotically homogeneous potentials.

Abstract

We extend the results of a previous paper on the Gross-Pitaevskii description of rotating Bose-Einstein condensates in two-dimensional traps to confining potentials of the form V(r) = r^s, $2<s <\infty$. Writing the coupling constant as $1/\epsilon^2$ we study the limit $\epsilon \to 0$. We derive rigorously the leading asymptotics of the ground state energy and the density profile when the rotation velocity \Omega tends to infinity as a power of $1/\epsilon$. The case of asymptotically homogeneous potentials is also discussed.