Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential
- Cite this article as:
- Sinai, Y.G. J Stat Phys (1987) 46: 861. doi:10.1007/BF01011146
The Schrödinger difference operator considered here has the form
whereV is aC2-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently smallɛ the operatorHɛ(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.
$$(H_\varepsilon (\alpha )\psi )(n) = - (\psi (n + 1) + \psi (n - 1)) + V(n\omega + \alpha )\psi (n)$$
Key wordsSchrödinger operatoreigenfunctioneigenvalueGreen's functioncontinued fraction
© Plenum Publishing Corporation 1987