Chaos and Lyapunov exponents in classical and quantal distribution dynamics

Details Chaos and Lyapunov exponents in classical and quantal distribution dynamics Chaos and Lyapunov exponents in classical and quantal distribution dynamics

1997-08-05

arxiv.org/abs/chao-dyn/9708003v1

Nonlinear Sciences

Chaotic Dynamics

5 RevTeX pages + 2 ps figs. Phys. Rev. E (to appear,'97)

Scientific paper

10.1103/PhysRevE.56.5174

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 which quantifies the rate at which chaotically evolving distributions acquire structure at increasingly smaller scales and which is generally larger than the maximal Lyapunov exponent $\lambda$ for trajectories. The approach is trajectory-independent and is therefore applicable to both classical and quantum mechanics. In the latter case we show that the $\hbar\to 0$ limit yields the classical, fully chaotic, result for the quantum cat map.

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