Closed orbits and spatial density oscillations in the circular billiard

Details Closed orbits and spatial density oscillations in the circular billiard Closed orbits and spatial density oscillations in the circular billiard

2009-05-04

arxiv.org/abs/0905.0347v3

J. Phys. A: Math. Theor. 42 (2009) 355210 (36pp)

Physics

Mathematical Physics

LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final version (v3) to be published in J. Phys. A

Scientific paper

We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed periodic and non-periodic orbits. We discuss their bifurcations under variation of the starting point r and derive analytical expressions for their properties such as actions, stability determinants, momentum mismatches and Morse indices. We present semiclassical calculations of the spatial density oscillations using a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev. Lett. 100 200408], employing standard uniform approximations from perturbation and bifurcation theory, and test the convergence of the closed-orbit sum.

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