Observation of Wigner-Dyson level statistics in a classically integrable system.

Abstract

Resonances in particle transmission through a 1D finite lattice are studied in the presence of a finite number of impurities. Although this is a one-dimensional system that is classically integrable and has no chaos, studying the statistical properties of the spectrum such as the level spacing distribution and the spectral rigidity shows the same statistics as the one obtained for chaotic systems. Using a dimensionless parameter that reflects the degree of state localization, we demonstrate how the transition from Poisson-level statistics to the Wigner-Dyson is affected by state localization. The resonance positions are calculated using both the Wigner-Smith time delay and a Siegert state method, which are in good agreement. Our results show the dependence of the level statistics on the localization length as it evolves from a Poisson distribution to Wigner-Dyson.