Distribution of level curvatures for the Anderson model at the localization-delocalization transition

We compute the distribution function of single-level curvatures, P(k), for a tight-binding model with site disorder, on a cubic lattice. In metals P(k) is very close to the predictions of the random-matrix theory (RMT). In insulators P(k) has a logarithmically normal form. At the Anderson localization-delocalization transition P(k) fits very well the proposed novel distribution P(k){∝}(1+k^μ{)}^{3/{{μ}}}$ with {μ}{}1.58, which approaches the RMT result for large k and is nonanalytical at small k. We ascribe such a nonanalyticity to the spatial multifractality of the critical wave functions. {} 1996 The American Physical Society.