Theory of quantum fluctuations in classically chaotic Hamiltonian systems

Abstract

In a number of numerical experiments it has been demonstrated that the initial growth of quantum variances of the dynamical variables for a chaotic trajectory is exponential in nature. This is a typical signature of classical chaos on a generic quantum dynamical feature. Based on the theory of multiplicative noise we have proposed a quantitative theory of this exponential divergence of quantum dispersions for general Hamiltonian systems, the rate constant being determined by the correlation function of the fluctuations of the curvature of the classical potential. The theory has been subsequently applied to a model driven double-well oscillator with detailed classical and quantum-mechanical calculation to verify the theoretical propositions