SPECTRAL DEGENERACY IN THE ONE-DIMENSIONAL ANDERSON PROBLEM - A UNIFORM EXPANSION IN THE ENERGY-BAND

A uniform quantitative description of the properties of the one-dimens ional Anderson model is obtained by mapping that problem onto an infin itely quasidegenerate master equation. This quasidegeneracy is identif ied as the source of the small-denominator problem encountered before in investigations of this problem. An appropriate quasidegenerate pert urbation theory is developed to obtain a uniform asymptotic expansion, in powers of the strength of the noise, for the probability distribut ion function of the ratio of the value of the wave function at neighbo ring sites. Well known results, such as those obtained by Thouless, Ka ppus and Wegner, and Derrida and co-workers are reproduced and systema tic corrections to these results as well as some more results are foun d. In particular, we find internal layers in the above-mentioned distr ibution function for values of the energy given by E = 2 cos pialpha w ith alpha rational. We also find crossovers in the behavior of the dis tribution function (and consequently in quantities derived from it) ne ar the band-edge and band-center regions. The properties of the model in the band-edge region were studied by us in detail in a previous pub lication [Phys. Rev. B 47, 1918 (1992)].