Classical versus quantum time evolution of (quasi-) probability densities at limited phase-space resolution

We study the interrelations between the classical (Frobenius-Perron) and the quantum (Husimi) propagator for phase-space (quasi-)probability densities in a Hamiltonian system displaying a mix of regular and chaotic behavior. We focus on common resonances of these operators which we determine by blurring phase-space resolution. We demonstrate that classical and quantum time evolution look alike if observed with a resolution much coarser than a Planck cell and explain how this similarity arises for the propagators as well as their spectra. The indistinguishability of blurred quantum and classical evolution implies that classical resonances can conveniently be determined from quantum mechanics and in turn become effective for decay rates of quantum correlations.