The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps

TL;DR

This paper derives the leading order energy and density asymptotics for a dilute, rotating Bose gas in an anharmonic trap in the Thomas-Fermi limit, revealing that the energy minimization simplifies despite complex wave function phases.

Contribution

It provides the first rigorous derivation of energy and density asymptotics for rapidly rotating Bose gases in anharmonic traps in the TF limit.

Findings

Leading order energy asymptotics derived

Density asymptotics characterized by a simple functional

Applicable in the limit of large coupling and rotation velocity

Abstract

Starting from the full many body Hamiltonian we derive the leading order energy and density asymptotics for the ground state of a dilute, rotating Bose gas in an anharmonic trap in the ` Thomas Fermi' (TF) limit when the Gross-Pitaevskii coupling parameter and/or the rotation velocity tend to infinity. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone.