Spectral properties and classical decays in quantum open systems

We study the relationship between the spectral properties of diffusive open quantum maps and the classical spectrum of Ruelle-Pollicott resonances. The leading resonances determine the asymptotic time regime for several quantities of interest - the linear entropy, the Loschmidt echo and the correlations of the initial state. A numerical method that allow an efficient calculation of the leading spectrum is developed using a truncated basis adapted to the dynamics.