Signatures of quantum chaos in complex wavefunctions describing open billiards

Abstract

We discuss signatures of quantum chaos in open chaotic billiards. Solutions for such a system are given by complex scattering wavefunctions ψ = u + iv when a steady current flows through the billiard. For slightly opened chaotic billiards the current distributions are simple and universal. It is remarkable that the resonant transmission through integrable billiards also gives the universal current distribution. Currents induced by the Rashba spin–orbit interaction can flow even in closed billiards. Wavefunction and current distributions for a chaotic billiard with weak and strong spin–orbit interactions have been derived and compared with numerics. Similarities with classical waves are considered. In particular we propose that the networks of electric resonance RLC circuits may be used to study wave chaos. However, being different from quantum billiards, there is a resistance from the inductors which gives rise to heat power and decoherence.