Periodic orbits and a correlation function for the semiclassical density of states

A principle of uniform density of periodic orbits in the phase space of a Hamiltonian system with bound classical motion is proposed and used to obtain information about the semiclassical quantum eigenvalue spectrum. It supplies a more refined statistic than the 'one state per Planck cell' rule for the average semiclassical density of states, namely the limiting behaviour of a certain correlation function of the density of states. Unlike the average, this correlation shows markedly different behaviour for systems with integrable and ergodic classical motion.