Topological Dependence of Universal Correlations in Multi-Parameter Hamiltonians

Details Topological Dependence of Universal Correlations in Multi-Parameter Hamiltonians Topological Dependence of Universal Correlations in Multi-Parameter Hamiltonians

1996-12-03

arxiv.org/abs/chao-dyn/9612007v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

15 pages, Latex, 5 postscript figures. To appear in Phys. Rev. E (December 1996)

Scientific paper

10.1103/PhysRevE.54.6207

Universality of correlation functions obtained in parametric random matrix theory is explored in a multi-parameter formalism, through the introduction of a diffusion matrix $D_{ij}(R)$, 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.

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