Topological dependence of universal correlations in multiparameter Hamiltonians.

Universality of correlation functions obtained in parametric random matrix theory is explored in a multi-parameter formalism, through the introduction of a diffusion matrix Dij(R), and compared to results from a multi-parameter chaotic model. We show that certain universal correlation functions in 1-d are no longer well defined by the metric distance between the points in parameter space, due to a global topological dependence on the path taken. By computing the density of diabolical points, which is found to increases quadratically with the dimension of the space, we find a universal measure of the density of diabolical points in chaotic systems. PACS numbers: 05.40+j, 05.45+b, 24.60.-k E–mail: [email protected]