Abstract:
In this work it is shown that all the eigenfunctions of the one-dimensional random Schröger operator H=−d2/dt2+q(t,ω), t∈R1, with random potential q(t,ω), ω∈Ω, of Markov type decrease exponentially with probability 1. This confirms an old conjecture of N. F. Mott which has been discussed many times in the physics literature.
Bibliography: 14 titles.
\Bibitem{Mol78}
\by S.~A.~Molchanov
\paper The structure of eigenfunctions of one-dimensional unordered structures
\jour Math. USSR-Izv.
\yr 1978
\vol 12
\issue 1
\pages 69--101
\mathnet{http://mi.mathnet.ru/eng/im1692}
\crossref{https://doi.org/10.1070/IM1978v012n01ABEH001841}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=486981}
\zmath{https://zbmath.org/?q=an:0386.34029|0401.34023}
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