On the degree of level repulsion

We argue that the degree of level repulsion can be determined by the two-level correlation function R₂(s), by explicitly showing the identity of the small s-behaviors of R₂(s) and the nearest-neighbor spacing distribution p(0;s). This may provide a new channel for the theoretical explanation of the mystery of the fractional power law observed numerically in the transition between integrability and chaos. Using this result, we propose to justify the level repulsion law by means of the long-time behavior of the quantum decoherence of a quantum-nondemolition coupling system.