Spectral Approach to Chaos and Quantum-Classical Correspondence in Quantum Maps

Correspondence in quantum chaotic systems is lost in short time scales. Introducing some noise we study the spectrum of the resulting coarse-grained propagator of density matrices. Some different methods to compute the spectrum are reviewed. The relationship between the eigenvalues of the coarse-grained superoperator and the classical Ruelle–Pollicott resonances is remarked on. As a consequence, classical decay rates in quantum time-dependent quantities appear.