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In previous work we have found a regime in ballistic quantum dots whereinterelectron interactions can be treated asymptotically exactly as theThouless number $g$ of the dot becomes very large. However, this work dependson some assumptions concerning the renormalization group and various propertiesof the dot obeying Random Matrix Theory predictions at scales of the order ofthe Thouless energy. In this work we test the validity of those assumptions byconsidering a particular ballistic dot, the Robnik-Berry billiard, numerically.We find that almost all of our predictions based on the earlier work are borneout, with the exception of fluctuations of certain matrix elements ofinteraction operators. We conclude that, at least in the Robnik-Berry billiard,one can trust the results of our previous work at a qualitative andsemi-quantitative level.Comment: 9 pages, 11 eps figure

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