Left–right Husimi representation of chaotic resonance states: invariance and factorization

Abstract For chaotic scattering systems we investigate the left–right Husimi representation, which combines left and right resonance states. We demonstrate that the left–right Husimi representation is invariant in the semiclassical limit under the corresponding closed classical dynamics, which we call quantum invariance. Furthermore, we show that it factorizes into a classical multifractal structure times universal quantum fluctuations. Numerical results for a dielectric cavity, the three-disk scattering system, and quantum maps confirm both the quantum invariance and the factorization.