Persistent currents for interacting electrons in ballistic/chaotic billiards*

We study persistent currents in a quantum billiard enclosing a magnetic flux $\phi$ by analytical and numerical methods. We concentrate on the family of Robnik-Berry billiards generated by conformal maps of the unit disk. We study the persistent current as a function of magnetic flux and parameters of the billiard in the chaotic regime. We include Fermi-liquid interactions in a mean-field approach, justified by the recent large-$N$ approach[1] for ballistic/chaotic quantum dots. [1] G. Murthy, R. Shankar, D. Herman, and H. Mathur, Phys. Rev. B 69, 075321 (2004); G. Murthy, R. Shankar, and H. Mathur, cond-mat/0411280.