Abstract
The integrated density of states has C∞-like singularities, ln|k(E)−k(E c )|=−|E−E c |−v/2 ϕ c (E), with ϕ c >0, a milder function at the edges of the spectral gaps which appear when the distribution function of the potentialdμ has a sufficiently large gap. The behaviour of ϕ c nearE c is determined by the local continuity properties ofdμ near the relevant edge: ϕ c (E)=O(1) ifdμ has an atom and ϕ=O(ln|E−E c |) if μ is (absolutely) continuous and power bounded.
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Mezincescu, G.A. Internal Lifschitz singularities of disordered finite-difference Schrödinger operators. Commun.Math. Phys. 103, 167–176 (1986). https://doi.org/10.1007/BF01464286
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DOI: https://doi.org/10.1007/BF01464286