Correlation Analysis of Quantum Fluctuations and Repulsion Characters of Classical Dynamics

The quantum level fluctuation in various systems has been shown to be characterized by the random matrix theory, and to be related to a regular-to-chaos transition in classical system. We present the qualitative analysis of the quantum and classical fluctuation properties by using correlation coefficients and variances. From this analysis we can derive a new phenomenological argument that the degree of level fluctuations are proportionally related with the degree of classical repulsion character observed in the unequal phase-space point spacing distributions on the Poincare section map. It is worth mentioning that our analysis of the level fluctuation differs from the random matrix approach in such a way that we excluded the probability assumption from our phenomenological consideration.