Trace
formula for level density of a spherical billiard
SHAM SUNDER MALIK, MANISHA DUDEJA and ASHOK
KUMAR JAIN
Department of Physics,
University of Roorkee, Roorkee 247 667, India
Department of Physics, G.N.D. University, Amritsar 143
005, India
MS received 6
November 1998; revised 17 May 1999
Abstract:
A trace formula for the
oscillating part of the level density for a spherical
billiard has been obtained in spherical polar
coordinates. The Jacobian of stability and the length
of the orbits are obtained from the classical
mechanics of the problem. The same formula is
applicable to both the planar and the diametric
orbits. Numerical results have been obtained with
this formula and compared with the results from exact
quantum theory, EBK quantization, and Balian and
Bloch.
Keywords. Semiclassical
methods; periodic orbit theory; trace formula;
spherical billiard.
PACS Nos 03.65.Sq;
03.65.Bz; 71.20.Ad
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