Recent Developments in Quantum Chaos of Mixed-Type Systems: A Mini Review

Abstract

We review recent developments in quantum chaos of generic systems, i.e. mixed-type systems whose classical counterparts have a divided phase space, where regular and chaotic regions coexist. We consider the energy level statistics, the Wigner and Husimi functions of the eigenstates, the localization properties of chaotic eigenstates in the phase space, their statistical properties and the power-law decay of the proportion of the mixed eigenstates in the semiclassical limit. These results confirm the prediction of the Principle of uniform semiclassical condensation (PUSC), which predicts the existence of either regular or chaotic Wigner and Husimi functions in the semiclassical limit, with vanishing fraction of the mixed states. These observations have been recently found in billiard systems, in quantum kicked top and in the Dicke model.