A RELATION BETWEEN BILLIARD GEOMETRY AND THE TEMPERATURE OF ITS EIGENVALUE GAS

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.