Dynamics of the Center of Mass in Arbitrary-Angle Rotating Bose-Einstein Condensates

Abstract

This paper investigates the dynamics of the center of mass in three-dimensional arbitrary-angle rotating Bose-Einstein condensates (ARotBECs), which are governed by the Gross-Pitaevskii equation (GPE) with an arbitrary-angle angular momentum rotation term. The second-order ordinary differential equations (ODEs) which govern the motion of the center of mass of ARotBECs are analytically solved. Subsequently, a novel numerical scheme, which is mass conservative — i.e. the Lagrangian multiplier-based Crank-Nicolson leap-frog (LagM-CNLF) method, integrated with Fourier pseudo-spectral spatial discretization, is proposed to efficiently and accurately simulate the GPE with arbitrary-angle rotation term. Finally, distinct motion patterns of the center of mass are systematically categorized based on analytical solutions and rigorously validated through direct numerical simulations of the GPE, demonstrating robust consistency between theoretical predictions and numerical computational results. The dynamics of quantized vortices is also studied to show the effectiveness of the LagM-CNLF method.