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Stochastic Schrödinger operators and Jacobi matrices on the strip

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We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ℂl so there are 2l Lyaponov exponents γ1≧...≧γl≧0≧γ l+1≧...≧γ2l =−γ1. Our results include the fact that if γ1=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j γ's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.

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Authors and Affiliations

  1. Department of Mathematics, University of Tokyo, Tokyo, Japan

    S. Kotani

  2. Division of Physics, Mathematics and Astronomy, California Institute of Technology, 91125, Pasadena, CA

    B. Simon

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  1. S. Kotani
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  2. B. Simon
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Communicated by T. Spencer

Research partially supported by USNSF under grant DMS-8416049

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Kotani, S., Simon, B. Stochastic Schrödinger operators and Jacobi matrices on the strip. Commun.Math. Phys. 119, 403–429 (1988). https://doi.org/10.1007/BF01218080

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  • DOI: https://doi.org/10.1007/BF01218080

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