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Spectral behavior of quasi periodic potentials

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Abstract

Spectral properties of Schrödinger operators of the typeH ɛ=−Δ+ɛV, where Δ is the Laplacian,V a quasiperiodic potential and ɛ a coupling constant, are developed.V is taken to be finite sum of exponentials with generic frequencies. For small ɛ 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 ɛ is increased.

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Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    P. Sarnak

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  1. P. Sarnak
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Communicated by B. Simon

Research supported in part by grant NSF MCS 7900813

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Sarnak, P. Spectral behavior of quasi periodic potentials. Commun.Math. Phys. 84, 377–401 (1982). https://doi.org/10.1007/BF01208483

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  • DOI: https://doi.org/10.1007/BF01208483

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