Recent experiments with cold atoms provide a significant step toward a better understanding of tunnelling when irregular dynamics is present at the classical level. In this paper, we lay out numerical studies which shed light on the previous experiments, help to clarify the underlying physics and have the ambition to be guidelines for future experiments.

11 pages, 9 figures, submitted to Phys. Rev. E. Figures of better quality can be found at http://www.phys.univ-tours.fr/~mouchet/