Topological dependence of universal correlations in multiparameter Hamiltonians.

Abstract

Universality of correlation functions obtained in parametric random matrix theory is explored in a multiparameter formalism, through the introduction of a diffusion matrix ${D}_{\mathrm{ij}}(\mathrm{R})$, and compared to results from a multiparameter chaotic model. We show that certain universal correlation functions in one dimension 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 increase quadratically with the dimension of the space, we find a universal measure of the density of diabolical points in chaotic systems.