Abstract
We discuss signatures of quantum chaos in open chaotic billiards. Solution for such a system are given by complex scattering wave functions ψ=u+iv provided that 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. Wave function and current distributions for chaotic billiard with weak and strong spin-orbit interactions have been derived and compared with numerics.
The complex scattering wave function can be specified by nodal points at which u=0, v=0. They have great physical significance since they are responsible for current vortices. We have calculated distribution functions for nearest distances between nodal points and found that there is a universal form for open chaotic billiards. The form coincides with the distribution for the Berry function and hence, it may be used as a signature of quantum chaos in open systems. All distributions agree well with numerically computed results for transmission through quantum chaotic billiards.
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.
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Sadreev, A.F., Berggren, KF. (2006). Signatures of quantum chaos in open chaotic billiards. In: Khanna, F., Matrasulov, D. (eds) Non-Linear Dynamics and Fundamental Interactions. NATO Science Series II: Mathematics, Physics and Chemistry, vol 213. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3949-2_5
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DOI: https://doi.org/10.1007/1-4020-3949-2_5
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