Abstract
We consider random discrete Schrödinger operators in a strip with a potentialV ω(n, α) (n a label in ℤ and α a finite label “across” the strip) andV ω an ergodic process. We prove thatH 0+V ω has only point spectrum with probability one under two assumptions: (1) Theconditional distribution of {V ω(n,α)} n=0,1;allα conditioned on {V ω} n≠0,1;allα has an absolutely continuous component with positive probability. (2) For a.e.E, no Lyaponov exponent is zero.
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Communicated by T. Spencer
Research partially supported by USNSF grant MCS-81-20833
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Simon, B. Localization in general one dimensional random systems, I. Jacobi matrices. Commun.Math. Phys. 102, 327–336 (1985). https://doi.org/10.1007/BF01229383
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DOI: https://doi.org/10.1007/BF01229383