Hans-Jürgen Stöckmann et al 1997 J. Phys. A: Math. Gen. 30 129 doi:10.1088/0305-4470/30/1/010
A relation between billiard geometry and the temperature of its eigenvalue gas
Hans-Jürgen Stöckmann, Ulrich Stoffregen and Michael Kollmann
Show affiliationsAccording to a conjecture of Yukawa the parametric motion of the eigenvalues of a chaotic system leads to a phase-space distribution proportional to 
where E is the energy of the eigenvalue gas and 
is its reciprocal temperature. To test the conjecture, in a first-step correspondence between the well known Pechukas - Yukawa level dynamics and that of a billiard with variable length is established. Next, is expressed in terms of the billiard geometry thus fixing the only free parameter of the model. Finally, experimental distributions of eigenvalue velocities, curvatures etc, obtained from Sinai microwave billiards are analysed in terms of the model. In all cases a quantitative agreement was found, apart from some small deviations caused by the dominating bouncing-ball orbit.
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Issue 1 (7 January 1997)
Received 18 January 1996, in final form 18 June 1996
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A relation between billiard geometry and the temperature of its eigenvalue gas
Hans-Jürgen Stöckmann et al 1997 J. Phys. A: Math. Gen. 30 129
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