A regular 1D system displaying signatures of quantum chaos

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, the statistical properties of the spectrum such as the level spacing distribution and the spectral rigidity are shown to be affected by the disorder in the lattice. Transmission resonance positions are calculated using both the Wigner-Smith time-delay and a Siegert state method, which are consistent. The level statistics of the resonances is found to fit different classless of the Brody distributions. The degree of level repulsion is found to correlate with a dimensionless parameter that measures the state localization. Despite the fact that this system is classically regular, GOE and GUE level statistics are seen to emerge for specific values of the localization length.