Gross-Pitaevskii Theory of the Rotating Bose Gas

TL;DR

This paper analyzes the ground state properties of a rotating Bose gas using the Gross-Pitaevskii functional, revealing symmetry breaking phenomena and their dependence on interaction strength and spin components.

Contribution

It proves symmetry breaking in the ground state of a rotating Bose gas and provides bounds on the critical coupling for this transition, including effects of spin components.

Findings

Ground state symmetry is broken at high interaction strengths.

Ground state energy varies with the number of spin components.

Explicit bounds on the critical coupling constant for symmetry breaking.

Abstract

We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the different components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking.