It is believed that the semi-Poisson function $P(S)=4S\exp(-2S)$ describes the normalized distribution of the nearest level-spacings $S$ for critical energy levels at the Anderson metal-insulator transition from quantum chaos to integrability, after an average over four obvious boundary conditions (BC) is taken (Braun { \it et} { \it al} \cite{ 1}). In order to check whether the semi-Poisson is the correct universal distribution at criticality we numerically compute it by integrating over all possible boundary conditions. We find that although $P(S)$ describes very well the main part of the obtained critical distribution small differences exist particularly in the large $S$ tail. The simpler crossover between the integrable ballistic and localized limits is shown to be universally characterized by a Gaussian-like $P(S)$ distribution instead.
Categories: cond-mat.mes-hall cond-mat.dis-nn