Multi-parameter continuation and collocation methods for rotating multi-component Bose–Einstein condensates

Abstract

We describe multi-parameter continuation methods combined with spectral collocation methods for computing numerical solutions of rotating two-component Bose-Einstein condensates (BECs), which are governed by the Gross-Pitaevskii equations (GPEs). Various types of orthogonal polynomials are used as the basis functions for the trial function space. A novel multi-parameter/multiscale continuation algorithm is proposed for computing the solutions of the governing GPEs, where the chemical potential of each component and angular velocity are treated as the continuation parameters simultaneously. The proposed algorithm can effectively compute numerical solutions with abundant physical phenomena. Numerical results on rotating two-component BECs are reported.

Efficient Continuation Methods for Computing Ground States of Quasi-2D Rotating Dipolar Bose-Einstein Condensates

“…Starting with φ2 ðx , yÞ = 0, (18) is the governing equation for a rotating BEC. By treating the chemical potential μ as the continuation parameter, we use an efficient continuation algorithm [19][20][21][22] to trace the ground state solution curve of (18) bifurcating at the first bifurcation point. The constraint condition (20) is set as the target point for the curve-tracking.…”