Anderson localization for the 1-D discrete Schrödinger operator with two-frequency potential

V. A. Chulaevsky; Ya G. Sinai

doi:10.1007/BF01217771

Anderson localization for the 1-D discrete Schrödinger operator with two-frequency potential

V. A. Chulaevsky, Ya G. Sinai

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

45 Scopus citations

Abstract

We prove the complete exponential localization of eigenfunctions for the 1-D discrete Schrödinger operators with quasi-periodic potentials having two basic frequencies. It is shown also that for such operators there is no forbidden zones in the spectrum, unlike the operators with one basic frequency.

Original language	English (US)
Pages (from-to)	91-112
Number of pages	22
Journal	Communications In Mathematical Physics
Volume	125
Issue number	1
DOIs	https://doi.org/10.1007/BF01217771
State	Published - Mar 1989

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01217771

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title = "Anderson localization for the 1-D discrete Schr{\"o}dinger operator with two-frequency potential",

abstract = "We prove the complete exponential localization of eigenfunctions for the 1-D discrete Schr{\"o}dinger operators with quasi-periodic potentials having two basic frequencies. It is shown also that for such operators there is no forbidden zones in the spectrum, unlike the operators with one basic frequency.",

author = "Chulaevsky, \{V. A.\} and Sinai, \{Ya G.\}",

year = "1989",

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AU - Chulaevsky, V. A.

AU - Sinai, Ya G.

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N2 - We prove the complete exponential localization of eigenfunctions for the 1-D discrete Schrödinger operators with quasi-periodic potentials having two basic frequencies. It is shown also that for such operators there is no forbidden zones in the spectrum, unlike the operators with one basic frequency.

AB - We prove the complete exponential localization of eigenfunctions for the 1-D discrete Schrödinger operators with quasi-periodic potentials having two basic frequencies. It is shown also that for such operators there is no forbidden zones in the spectrum, unlike the operators with one basic frequency.

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Anderson localization for the 1-D discrete Schrödinger operator with two-frequency potential

Abstract

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