Spectral statistics of the two-body random ensemble revisited - art. no. 026204

Using longer spectra we reanalyze spectral properties of the two-body rando m ensemble studied 30 years ago. At the center of the spectra the old resul ts are largely confirmed, and we show that the nonergodicity is essentially due to the variance of the lowest moments of the spectra. The longer spect ra 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 problem s of unfolding in more detail. With a Gaussian unfolding of each spectrum t he nearest-neighbor spacing distribution between ground state and first exi ted state is shown to be stable. Using such an unfolding the distribution t ends toward a semi-Poisson distribution for longer spectra. For comparison with the nuclear table ensemble we could use such unfolding obtaining simil ar results as in the early papers, but an ensemble with realistic splitting gives reasonable results if we just normalize the spacings in accordance w ith the procedure used for the data.