Spectral behavior of quasi periodic potentials

P. Sarnak

doi:10.1007/BF01208483

Spectral behavior of quasi periodic potentials

P. Sarnak

Research output: Contribution to journal › Article › peer-review

59 Scopus citations

Abstract

Spectral properties of Schrödinger operators of the type H_e{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 language	English (US)
Pages (from-to)	377-401
Number of pages	25
Journal	Communications In Mathematical Physics
Volume	84
Issue number	3
DOIs	https://doi.org/10.1007/BF01208483
State	Published - Sep 1982
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01208483

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@article{86613901128c4e209a1cae8f7aafaa17,

title = "Spectral behavior of quasi periodic potentials",

abstract = "Spectral properties of Schr{\"o}dinger 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.",

author = "P. Sarnak",

year = "1982",

month = sep,

doi = "10.1007/BF01208483",

language = "English (US)",

volume = "84",

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journal = "Communications In Mathematical Physics",

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publisher = "Springer New York",

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T1 - Spectral behavior of quasi periodic potentials

AU - Sarnak, P.

PY - 1982/9

Y1 - 1982/9

N2 - 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.

AB - 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.

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U2 - 10.1007/BF01208483

DO - 10.1007/BF01208483

M3 - Article

AN - SCOPUS:0000548765

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VL - 84

SP - 377

EP - 401

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -

Spectral behavior of quasi periodic potentials

Abstract

All Science Journal Classification (ASJC) codes

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