Mv. Berry et Jp. Keating, PERSISTENT CURRENT FLUX CORRELATIONS CALCULATED BY QUANTUM CHAOLOGY, Journal of physics. A, mathematical and general, 27(18), 1994, pp. 6167-6176
We consider classically chaotic systems with the topology of a ring th
readed by quantum flux phi. Using semiclassical asymptotics, we calcul
ate the flux-averaged autocorrelation function C(phi) of slopes of the
energy levels (persistent currents), normalized by the mean level spa
cing, for flux values differing by phi. Our result furnishes the unifo
rm approximation C(phi) approximate to - sin(2)(pi phi) - 1/w(2)/[sin
(2)(pi phi) + 1/w(2)](2). Here w*, the RMS winding number of the clas
sical periodic orbits whose period is connected by Heisenberg's relati
on to the mean level spacing, is a (large) semiclassical parameter, of
order 1/(h) over bar((D-1)/2) for a system with D freedoms.