Quantum correlations from Brownian diffusion of chaotic level-spacings
S. N. Evangelou, D. E. Katsanos
Abstract
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.
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