Boundary Conditions at the Mobility Edge

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 Σ²(E) also depends on the boundary conditions, but this dependence vanishes at high energy E. This implies that the multifractal exponent D₂ of the participation ratio of wave functions in the bulk is not affected by the boundary conditions.