Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems

URN to cite this document:: urn:nbn:de:bvb:355-epub-19011
DOI to cite this document:: 10.5283/epub.1901

Gutiérrez, Martha ; Richter, Klaus ; Sugita, Ayumu ; Brack, Matthias

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Date of publication of this fulltext: 05 Aug 2009 13:34

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Abstract

We present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a Hamiltonian quantum system defined by two coupled quartic oscillators, which on the classical level exhibits mixed phase space dynamics. We show that the signature of a pitchfork bifurcation is two-fold: beside the known effect of an enhanced periodic orbit ...