Stochastic parametric amplification due to higher order correlations: A perturbative approach to non-Abelian effects in time ordering

In this paper, we use quantum-mechanical formalism to describe the time evolution of a classical dynamical system with fluctuating parameters. By appropriate choice of ''interaction picture representation,'' and the use of the Baker-Campbell-Hausdorff formula in the chronological time ordered evolution, we have obtained analytical expressions for the Lyapunov exponent of the energy evolution of the dynamical system. Our approach proved to be very powerful in handling either stochastic or highly correlated processes. The approach lends itself to generalizations for use in a wide field of applications