  We consider unitary evolution of finite bipartite quantum systems and study
time dependence of purity for initial cat states -- coherent superpositions of
Gaussian wave-packets. We derive explicit formula for purity in systems with
nonzero time averaged coupling, a typical situation for systems where an
uncoupled part of the Hamiltonian is Liouville integrable. Previous analytical
studies have been limited to harmonic oscillator systems but with our theory we
are able to derive analytical results for general integrable systems. Two
regimes are clearly identified, at short times purity decays due to decoherence
whereas at longer times it decays because of relaxation.
