Abstract
The Schrödinger difference operator considered here has the form
whereV is aC 2-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently smallɛ the operatorH ɛ(α) has for a.e.α a pure point spectrum. The corresponding eigenfunctions decay exponentially outside a finite set. The integrated density of states is an incomplete devil's staircase with infinitely many flat pieces.
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Sinai, Y.G. Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential. J Stat Phys 46, 861–909 (1987). https://doi.org/10.1007/BF01011146
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DOI: https://doi.org/10.1007/BF01011146