Abstract
The quantum to classical transition for a system depends on many parameters, including a scale length for its action, , a measure of its coupling to the environment, , and, for chaotic systems, the classical Lyapunov exponent, . We propose measuring the proximity of quantum and classical evolutions as a multivariate function of and searching for transformations that collapse this hypersurface into a function of a composite parameter . 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.
- Received 11 June 2002
DOI:https://doi.org/10.1103/PhysRevLett.90.014103
©2003 American Physical Society