Critical quantum chaos and the one-dimensional Harper model

We obtain numerically a scale-invariant distribution of the bandwidths S fo r the critical Harper model, which is closely described by a semi-Poisson P (S) = 4S exp(-2S) curve. After a suitable unfolding: of spectra, derived fr om different boundary conditions, a semi-Poisson level spacing distribution and a sub-Poisson linear number variance are deduced from the bandwidth di stribution. The obtained results support possible universality of the criti cal spectral statistics and suggest its connection to spectral multifractal ity.