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Boundary conditions at the mobility edge

D. Braun·G. Montambaux·M. Pascaud
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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 $Σ^2(E)$ 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.

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D. Braun, G. Montambaux, M. Pascaud. 1998-05-27. Boundary conditions at the mobility edge. https://doi.org/10.1103/physrevlett.81.1062

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