Hj. Stockmann et al., A RELATION BETWEEN BILLIARD GEOMETRY AND THE TEMPERATURE OF ITS EIGENVALUE GAS, Journal of physics. A, mathematical and general, 30(1), 1997, pp. 129-141
According to a conjecture of Yukawa the parametric motion of the eigen
values of a chaotic system leads to a phase-space distribution proport
ional to exp(-beta E) where E is the energy of the eigenvalue gas and
beta is its reciprocal temperature. To test the conjecture, in a first
-step correspondence between the well known Pechukas-Yukawa level dyna
mics and that of a billiard with variable length is established. Next,
beta is expressed in terms of the billiard geometry thus fixing the o
nly free parameter of the model. Finally, experimental distributions o
f eigenvalue velocities, curvatures etc, obtained from Sinai microwave
billiards are analysed in terms of the model. In all cases a quantita
tive agreement was found, apart from some small deviations caused by t
he dominating bouncing-ball orbit.