Persistent current flux correlations calculated by quantum chaology

We consider classically chaotic systems with the topology of a ring threaded by quantum flux phi . Using semiclassical asymptotics, we calculate the flux-averaged autocorrelation function C( phi ) of slopes of the energy levels (persistent currents), normalized by the mean level spacing, for flux values differing by phi . Our result furnishes the uniform approximation C( phi ) approximately=-(sin 2 ( pi phi )-1/w* 2 )/(sin 2 ( pi phi )+1/w* 2 ) 2 . Here w*, the RMS winding number of the classical periodic orbits whose period is connected by Heisenberg's relation to the mean level spacing, is a (large) semiclassical parameter, of order 1/h(cross) (D-1 2/) for a system with D freedoms.