Splitting of the low Landau levels into a set of positive Lebesgue measure under small periodic perturbations

E. I. Dinaburg, Ya G. Sinai, A. B. Soshnikov

Research output: Contribution to journalArticle

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Abstract

We study the spectral properties of a two-dimensional Schrödinger operator with a uniform magnetic field and a small external periodic field: (formula presented) where V(x,y) = V0(y) + ε1V1(x,y), and ε0, ε1 are small parameters. Representing Lε0 as the direct integral of one-dimensional quasi-periodic difference operators with long-range potential and employing recent results of E.I.Dinaburg about Anderson localization for such operators (we assume 2π/B to be typical irrational) we construct the full set of generalised eigenfunctions for the low Landau bands. We also show that the Lebesgue measure of the low bands is positive and proportional in the main order to ε0.

Original languageEnglish (US)
Pages (from-to)559-575
Number of pages17
JournalCommunications In Mathematical Physics
Volume189
Issue number2
DOIs
StatePublished - Jan 1 1997

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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