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Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems

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Gutiérrez, Martha ; Richter, Klaus ; Sugita, Ayumu ; Brack, Matthias
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PDF - Accepted Version
arXiv PDF (10.01.2007)
PDF - Submitted Version
arXiv PDF (23.10.2006)
Date of publication of this fulltext: 05 Aug 2009 13:34


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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