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Behavior of the density of states in one-dimensional disordered systems near the edges of the spectrum

S. A. Gredeskul, L. A. Pastur


Abstract: Singularities of the density of states in one-dimensional disordered systems near the spectrum bounds have been studied. It is shown that there exist two types of the true bounds, fluctuational and stable ones. The density of states in the neighbourhood of a fluctuational bound is determined by probabilistic properties of the problem. Near a stable spectrum bound the density of states as a function of the energy parameter possisses an universal square root singularity. Specific distinctions of the problem influence only the magnitude of the coefficient of this singularity.

Received: 29.04.1974

 English version: Theoretical and Mathematical Physics, 1975, 23:1, 404–409