2017/01/05 by Carlos García-Azpeitia, García-Azpeitia, C., Dmitry E. Pelinovsky +1 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Strong Light-Matter Interactions #Physics of Superconductivity and Magnetism
paper · pdf · doi:10.48550/arxiv.1701.01494
We analyze global bifurcations along the family of radially symmetric vortices in the Gross--Pitaevskii equation with a symmetric harmonic potential and a chemical potential μ under the steady rotation with frequency Ω. The families are constructed in the small-amplitude limit when the chemical potential μ is close to an eigenvalue of the Schrödinger operator for a quantum harmonic oscillator. We show that for Ω near 0, the Hessian operator at the radially symmetric vortex of charge m0∈ℕ has m0(m0+1)/2 pairs of negative eigenvalues. When the parameter Ω is increased, 1+m0(m0-1)/2 global bifurcations happen. Each bifurcation results in the disappearance of a pair of negative eigenvalues in the Hessian operator at the radially symmetric vortex. The distributions of vortices in the bifurcating families are analyzed by using symmetries of the Gross--Pitaevskii equation and the zeros of Hermite--Gauss eigenfunctions. The vortex configurations that can be found in the bifurcating families are the asymmetric vortex (m0 = 1), the asymmetric vortex pair (m0 = 2), and the vortex polygons (m0 ≥ 2).