T Bartsch et al 1999 J. Phys. A: Math. Gen. 32 3013 doi:10.1088/0305-4470/32/16/010
Significance of ghost orbit bifurcations in semiclassical spectra
T Bartsch
, J Main and G Wunner
Gutzwiller's trace formula for the semiclassical density of states in a chaotic system diverges near bifurcations of periodic orbits, where it must be replaced with uniform approximations. It is well known that, when applying these approximations, complex predecessors of orbits created in the bifurcation (`ghost orbits') can produce pronounced signatures in the semiclassical spectra in the vicinity of the bifurcation. It is the purpose of this paper to demonstrate that these ghost orbits can also undergo bifurcations, resulting in complex, nongeneric bifurcation scenarios. We do so by studying an example taken from the diamagnetic Kepler problem, namely the period quadrupling of the balloon orbit. 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.
- PACS
- MSC
-
81Q50 Quantum chaos (See also 37Dxx)
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
-
Issue 16 (23 April 1999)
Received 22 December 1998, in final form 4 February 1999
-
Significance of ghost orbit bifurcations in semiclassical spectra
T Bartsch et al 1999 J. Phys. A: Math. Gen. 32 3013
-
NMR characterization of spin-½ alternating antiferromagnetic chains in the high-pressure phase of (V O)2P2O7
J Kikuchi et al 2004 J. Phys.: Condens. Matter 16 L167
-
The free energy of a collapsing branched polymer
N Madras et al 1990 J. Phys. A: Math. Gen. 23 5327
-
Warped Ionized Hydrogen in the Galaxy
J. C. Cersosimo et al. 2009 ApJ 699 469
-
Photodestruction of Relevant Interstellar Molecules in Ice Mixtures
Hervé Cottin et al. 2003 ApJ 590 874
-
The reduction of the closest disentangled states
Satoshi Ishizaka 2002 J. Phys. A: Math. Gen. 35 8075
-
The Great Observatories Origins Deep Survey: Initial Results from Optical and Near-Infrared Imaging
M. Giavalisco et al 2004 ApJ 600 L93
-
VLA H53α Radio Recombination Line Observations of the Ultraluminous Infrared Galaxy Arp 220
C. A. Rodríguez-Rico et al. 2005 ApJ 633 198
-
A Theoretical Recalibration of the Extragalactic H II Region Sequence
M. A. Dopita et al. 2000 ApJ 542 224
-
Quasi-periodic Green's functions of the Helmholtz and Laplace equations
Alexander Moroz 2006 J. Phys. A: Math. Gen. 39 11247
Users also read
What's this?Related review articles
What's this?- Integrable structure of box–ball systems: crystal, Bethe ansatz, ultradiscretization and tropical geometry
- Trajectory attractors of equations of mathematical physics
- Spectral problems in open quantum chaos