Spectral statistics of the two-body random ensemble revisited

Abstract

Using longer spectra we reanalyze spectral properties of the two-body random ensemble studied 30 years ago. At the center of the spectra the old results are largely confirmed, and we show that the nonergodicity is essentially due to the variance of the lowest moments of the spectra. The longer spectra allow us to test and reach the limits of validity of French's correction for the number variance. At the edge of the spectra we discuss the problems of unfolding in more detail. With a Gaussian unfolding of each spectrum the nearest-neighbor spacing distribution between ground state and first exited state is shown to be stable. Using such an unfolding the distribution tends toward a semi-Poisson distribution for longer spectra. For comparison with the nuclear table ensemble we could use such unfolding obtaining similar results as in the early papers, but an ensemble with realistic splitting gives reasonable results if we just normalize the spacings in accordance with the procedure used for the data.