Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2006-10-19
J. Phys. A: Math. Theor. 40 (2007) 1525-1543
Nonlinear Sciences
Chaotic Dynamics
LaTex, 25 pp., 14 Figures (26 *.eps files); final version 3, to be published in Journal of Physics A
Scientific paper
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 contribution due to its peculiar $\hbar$-dependence at the bifurcation, we demonstrate that the orbit pair born {\em at} the bifurcation gives rise to distinct deviations from universality slightly {\em above} the bifurcation. This requires a semiclassical treatment beyond the so-called diagonal approximation. Our semiclassical predictions for both the coarse-grained density of states and the spectral rigidity, are in excellent agreement with corresponding quantum-mechanical results.
Brack Matthias
Guti{é}rrez Marta
Richter Klaus
Sugita Ayumu
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