Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential

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Abstract

The Schrödinger difference operator considered here has the form {Mathematical expression} where V is a C2-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently small e{open} the operator He{open}(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.

Original languageEnglish (US)
Pages (from-to)861-909
Number of pages49
JournalJournal of Statistical Physics
Volume46
Issue number5-6
DOIs
StatePublished - Mar 1 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Keywords

  • Green's function
  • Schrödinger operator
  • continued fraction
  • eigenfunction
  • eigenvalue

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