Spectral behavior of quasi periodic potentials

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Abstract

Spectral properties of Schrödinger operators of the type He{open}=-Δ+e{open}V, where Δ is the Laplacian, V a quasiperiodic potential and e{open} a coupling constant, are developed. V is taken to be finite sum of exponentials with generic frequencies. For small e{open} a strong stability is shown. On the other hand, examples (in the finite diffeence case) are given, for which a transition in the type of spectrum occurs, as e{open} is increased.

Original languageEnglish (US)
Pages (from-to)377-401
Number of pages25
JournalCommunications In Mathematical Physics
Volume84
Issue number3
DOIs
StatePublished - Sep 1 1982
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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