Quantum correlations from Brownian diffusion of chaotic level-spacings
  Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the level-spacings while the integrability to chaos transition becomes a change from Poisson to Gauss statistics for the level-spacing increments. This universal nature of quantum chaotic spectral correlations is numerically demonstrated for eigenvalues from random tight binding lattices and for zeros of the Riemann zeta function. 
S.N. Evangelou and D.E. Katsanos