Parameter scaling in the decoherent quantum-classical transition for chaotic systems

The quantum to classical transition for a system depends on many parameters, including a scale length for its action, (h) over bar, a measure of its coupling to the environment, D, and, for chaotic systems, the classical Lyapunov exponent, lambda. We propose measuring the proximity of quantum and classical evolutions as a multivariate function of ((h) over bar,lambda,D) and searching for transformations that collapse this hypersurface into a function of a composite parameter zeta=(h) over bar (alpha)lambda(beta)D(gamma). We report results for the quantum Cat Map and Duffing oscillator, showing accurate scaling behavior over a wide parameter range, indicating that this may be used to construct universality classes for this transition.