Abstract
We investigate the spectrum of Schrödinger operatorsH ω of the type:H ω=−Δ+∑q i (ω)f(x−x i +ζ i (ω))(q i (ω) and ζ i (ω) independent identically distributed random variables,i∈ℤd). We establish a strong connection between the spectrum ofH ω and the spectra of deterministic periodic Schrödinger operators. From this we derive a condition for the existence of “forbidden zones” in the spectrum ofH ω. For random one- and three-dimensional Kronig-Penney potentials the spectrum is given explicitly.
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Communicated by Ya. G. Sinai
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Kirsch, W., Martinelli, F. On the spectrum of Schrödinger operators with a random potential. Commun.Math. Phys. 85, 329–350 (1982). https://doi.org/10.1007/BF01208718
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DOI: https://doi.org/10.1007/BF01208718