Numerical Investigation of Vortices’ Formation in the Rotating Bose-Einstein Condensates

Sammanfattning

This study focuses on numerically investigating the emergence of vortices in the ground stateofthe rotating Bose-Einstein Condensates (BECs) within a Gross-Pitaevskii framework. Ourprimary objective is to identify an indicator that correlates vortex formation with the rotationaleffects of the BEC. We explore both numerically and analytically the H1 and H2 norms of theground states, demonstrating that the proposed indicator effectively describes the bounds ofthese norms. Additionally, it serves as the mesh step required for the finite element method toaccurately capture the appearance of vortices and provide the ground state.