Uniform semiclassical approximations for umbilic bifurcation catastrophes

Abstract

Gutzwiller's trace formula for the semiclassical density of states diverges at the bifurcation points of periodic orbits and has to be replaced with uniform semiclassical approximations. We present a method to derive these expressions from the standard representations of the elementary catastrophes and to directly relate the uniform solutions to classical periodic orbit parameters, thereby circumventing the numerical application of normal form theory. The technique allows an easy handling of ungeneric bifurcations with corank 2 such as the umbilic catastrophes and is demonstrated on a hyperbolic umbilic in the diamagnetic Kepler problem.

4 pages, 4 figures, REVTEX, Phys. Rev. E (in press)

References in corpus (3)

• Bifurcations of Periodic Orbits and Uniform Approximations
• Semiclassical interference of bifurcations
• Semiclassical spectra from periodic-orbit clusters in a mixed phase space

Cited by in corpus (6)

• Use of Harmonic Inversion Techniques in Semiclassical Quantization and Analysis of Quantum Spectra
• Significance of Ghost Orbit Bifurcations in Semiclassical Spectra
• Ghost orbits in the diamagnetic hydrogen spectrum using harmonic inversion
• Uniform approximations for non-generic bifurcation scenatios including bifurcations of ghost orbits
• Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits
• Uniform semiclassical approximations on a topologically non-trivial configuration space: The hydrogen atom in an electric field