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Prog. Theor. Phys. Supplement No.139 (2000) pp. 429-436
Ghost Orbit Bifurcations in Semiclassical Spectra
Thomas Bartsch,
Jörg Main and
Günter Wunner
Institut für Theoretische Physik 1, Universität Stuttgart
D-70550 Stuttgart, Germany
Abstract:
Gutzwiller's semiclassical trace formula for the density of states in a
chaotic system diverges near bifurcations of periodic orbits, where it must
be replaced by a modified one with uniform approximations.
It is well known that, when
applying these approximations, complex predecessors of orbits created in the
bifurcation (“ghost orbits”) can produce clear signatures in the
semiclassical spectra. We demonstrate that these orbits themselves can
undergo bifurcations, resulting in complex, non-generic bifurcation
scenarios. We do so by studying an example taken from the Diamagnetic Kepler
Problem. By application of normal form theory, we construct an analytic
description of the complete bifurcation scenario, which is then used to
calculate the pertinent uniform approximation. The ghost orbit bifurcation
turns out to produce signatures in the semiclassical spectrum in much the same
way as a bifurcation of real orbits would.
URL :
http://ptp.ipap.jp/link?PTPS/139/429/
DOI : 10.1143/PTPS.139.429
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