Bifurcations and random matrix theory
Fachbereich Physik, Philipps Universität
Marburg - D-35032 Marburg, Germany
2 Komplex Rendszerek Fizikája Tanszék, Eötvös Loránd Tudmányegyetem H-1518 Budapest Pf. 32, Hungary
Accepted: 11 January 2001
The divergence of semiclassical amplitudes at periodic orbit bifurcations has strong effects on long-range spectral statistics. We discuss the statistical weight of such effects in parameter space, using as an example the quantised standard map as a function of the kicking strength. The parameter interval affected by saddle-node bifurcations is independent of and determined by classical dynamics. In the distribution P(t) of the traces of the evolution operator the bifurcations contribute an algebraically decaying part that exceeds the exponentially decaying RMT part for large traces. Specifically, for saddle-node bifurcations up to .
PACS: 05.45.Mt – Semiclassical chaos ("quantum chaos") / 03.65.Sq – Semiclassical theories and applications
© EDP Sciences, 2001