Quantal Lyapunov exponent

Abstract

A quantal analogue of the maximum Lyapunov exponent α q is defined on the basis of the Q-representation of the density operator. Its usefulness is examined for typical chaotic non-autonomous systems with 2 degrees of freedom. For a homogeneously unstable system this exponent agrees quite well with the classical one, but it is much less than the classical exponent for inhomogeneously unstable systems. In both cases, “orbital instability” is observed up to the characteristic time τ c≈log( A R/ħ)α q, where A R is the area of the chaotic region in the phase space and ħ the Planck constant.