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Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems

URN to cite this document:
urn:nbn:de:bvb:355-epub-19011
Gutiérrez, Martha ; Richter, Klaus ; Sugita, Ayumu ; Brack, Matthias
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PDF - Accepted Version
arXiv PDF (10.01.2007)
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arXiv PDF (23.10.2006)
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Date of publication of this fulltext: 05 Aug 2009 13:34



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 ...

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