  In this work, we study the out-of-equilibrium many-body tunneling dynamics of
a Bose-Einstein condensate in a two-dimensional radial double well. We
investigate the impact of interparticle repulsion and compare the influence of
angular momentum on the many-body tunneling dynamics. Accurate many-body
dynamics are obtained by solving the full many-body Schr\"odinger equation. We
demonstrate that macroscopic vortex states of definite total angular momentum
indeed tunnel and that, even in the regime of weak repulsions, a many-body
treatment is necessary to capture the correct tunneling dynamics. As a general
rule, many-body effects set in at weaker interactions when the tunneling system
carries angular momentum.
