Ballistic chaotic quantum dots with interactions: A numerical study of the Robnik-Berry billiard

In previous work we have found a regime in ballistic quantum dots where interelectron interactions can be treated asymptotically exactly as the Thouless number g of the dot becomes very large. However, the results of the previous work depend on some assumptions concerning the renormalization group and various properties of the dot obeying random matrix theory predictions at scales of the order of Thouless energy. In the present work we test the validity of those assumptions by considering a particular ballistic dot, the Robnik-Berry billiard, numerically. While we find that many of our earlier predictions are borne out, some global aspects of our phase diagram need to be modified. With those modifications we conclude that, at least in the Robnik-Berry billiard, one can trust the results of our previous work at a qualitative and semiquantitative level.