Abstract
In the multi-dimensional case it is shown that the increase of the topological support of the probability measure describing the randomness of potentials implies the increase of the spectrum. In the one-dimensional case the converse statement for the absolutely continuous spectrum is valid. Especially the spectrum (in general dimension) and the absolutely continuous spectrum (in one-dimension) are determined only by the topological support of the random potentials.
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References
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Communicated by B. Simon
Research partially supported by the USNSF under grant MCS-81-20833
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Kotani, S. Support theorems for random Schrödinger operators. Commun.Math. Phys. 97, 443–452 (1985). https://doi.org/10.1007/BF01213407
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DOI: https://doi.org/10.1007/BF01213407