Bohr billiard: Decay in the chaotic Hamiltonian system with two integrals of motion

The two-dimensional system of two identical hard disks moving freely within the circular potential well (billiard) of finite depth is studied as an example of the Hamiltonian chaotic system with two integrals of motion-the total energy and the total angular momentum. The kinetics of decay in the ensemble of such systems with fixed values of integrals of motion can be described by the exponential law, if the energy is lower than the threshold of two-particle decay. For this range the rate of the decay is calculated analytically as a function of energy, angular momentum, and the ratio of disk and billiard radii. The numerical calculations confirm the theoretical estimate of the decay rate in the wide range of its values.