Brack, Matthias and Roccia, J (2009) Closed orbits and spatial density oscillations in the circular billiard. .
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Other URL: http://arxiv.org/abs/0905.0347
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 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 200408], employing standard uniform approximations from perturbation and bifurcation theory, and test the convergence of the closed-orbit sum.
|Institutions:||Physics > Institute of Theroretical Physics > Chair Professor Schäfer > Group Matthias Brack|
|Projects:||Graduiertenkolleg Nichtlinearität und Nichtgleichgewicht|
|Subjects:||500 Science > 530 Physics|
|Refereed:||Yes, this version has been refereed|
|Created at the University of Regensburg:||Yes|
|Deposited On:||25 May 2009 13:22|
|Last Modified:||17 Nov 2009 04:07|