Effects of Coulomb interaction on the density of states in open chaotic billiards

The density of states (DOS) in open chaotic: billiards is studied semiclass ically in the presence of Coulomb interaction. The exchange and Hartree cor rections to the DOS as a function of energy epsilon relative to the Fermi e nergy are calculated at zero temperature including higher-order interaction effects. It is shown that the DOS decreases with increasing \epsilon\ in t he low-energy regime and begins to increase around \epsilon\ approximate to t(B)(-1), where t(B) is the classical escape time. For t(B)(-1) much less than \epsilon\, a logarithmic increase of the DOS is shown to appear. This anomalous dependence is due to competition between the exchange and Hartree corrections.