Persistent currents in mesoscopic cavities and the effect of level   crossings as random variables
  In the present article we perform analytical and numerical calculations related to persistent currents in 2D isolated mesoscopic annular cavities threaded by a magnetic flux. The system considered has a high number of open channels and therefore the single particle spectrum exhibits many level crossings as the flux varies. We determine the effect of the distribution of level crossings in the typical persistent current. 
A. J. Fendrik and M. J. Sanchez