CHAOS AND LYAPUNOV EXPONENTS IN CLASSICAL AND QUANTAL DISTRIBUTION DYNAMICS

We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions rho(p,q). Of particular interest is lambda(2), an exponent that quantifies the fate at which chaotically evolving distributions acquire structure at increasingly s maller scales and is generally larger than the maximal Lyapunov expone nt lambda for trajectories. The approach is trajectory independent and is therefore applicable to both classical and quantum mechanics. In t he latter case we show that the (h) over bar-->0 limit yields the clas sical, fully chaotic, result for the quantum cat map.