Vortices and Spontaneous Symmetry Breaking in Rotating Bose Gases

TL;DR

This paper rigorously proves the emergence of quantized vortices and spontaneous symmetry breaking in rotating dilute Bose gases, connecting many-body quantum mechanics with the nonlinear Gross-Pitaevskii equation.

Contribution

It provides a rigorous mathematical proof linking the many-body Schrödinger equation to vortex formation and symmetry breaking in rotating Bose gases.

Findings

Quantized vortices appear in the ground state.

Spontaneous symmetry breaking occurs due to vortices.

Results connect many-body physics with nonlinear PDE models.

Abstract

We present a rigorous proof of the appearance of quantized vortices in dilute trapped Bose gases with repulsive two-body interactions subject to rotation, which was obtained recently in joint work with Elliott Lieb. Starting from the many-body Schroedinger equation, we show that the ground state of such gases is, in a suitable limit, well described by the nonlinear Gross-Pitaevskii equation. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.