Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2004-11-10
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 pages, 11 eps figures
Scientific paper
10.1103/PhysRevB.72.075364
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, this work depends on some assumptions concerning the renormalization group and various properties of the dot obeying Random Matrix Theory predictions at scales of the order of the Thouless energy. In this work we test the validity of those assumptions by considering a particular ballistic dot, the Robnik-Berry billiard, numerically. We find that almost all of our predictions based on the earlier work are borne out, with the exception of fluctuations of certain matrix elements of interaction operators. We conclude that, at least in the Robnik-Berry billiard, one can trust the results of our previous work at a qualitative and semi-quantitative level.
Mathur Harsh
Murthy Ganpathy
Shankar Raji
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