Closed orbits and spatial density oscillations in the circular billiard
Abstract
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.
Cite
@article{arxiv.0905.0347,
title = {Closed orbits and spatial density oscillations in the circular billiard},
author = {Matthias Brack and Jérôme Roccia},
journal= {arXiv preprint arXiv:0905.0347},
year = {2015}
}
Comments
LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final version (v3) to be published in J. Phys. A