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 ${\Sigma }^2\left(E\right)$ 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.