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, ℏ, a measure of its coupling to the environment, D, and, for chaotic systems, the classical Lyapunov exponent, λ. We propose measuring the proximity of quantum and classical evolutions as a multivariate function of (ℏ,λ,D) and searching for transformations that collapse this hypersurface into a function of a composite parameter ζ=ℏ^αλ^βD^γ. 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.