Effects of Coulomb Interaction on the Density of States in Open Chaotic Billiards

Abstract

The density of states (DOS) in open chaotic billiards is studied semiclassically in the presence of Coulomb interaction. The exchange and Hartree corrections to the DOS as a function of energy ε relative to the Fermi energy are calculated at zero temperature including higher-order interaction effects. It is shown that the DOS decreases with increasing | ε | in the low-energy regime and begins to increase around | ε |≈ t B -1 , where t B is the classical escape time. For t B -1 ≪| ε |, a logarithmic increase of the DOS is shown to appear. This anomalous ε -dependence is due to competition between the exchange and Hartree corrections.