Boundary conditions at the mobility edge

Abstract

It is shown that the universal behavior of the spacing distribution of nearest energy levels at the metal--insulator Anderson transition is indeed dependent on the boundary conditions. The spectral rigidity $\Sigma^2(E)$ also depends on the boundary conditions but this dependence vanishes at high energy $E$. This implies that the multifractal exponent $D_2$ of the participation ratio of wave functions in the bulk is not affected by the boundary conditions.