Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential

Ya G. Sinai

doi:10.1007/BF01011146

Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential

Ya G. Sinai

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

183 Scopus citations

Abstract

The Schrödinger difference operator considered here has the form {Mathematical expression} where V is a C²-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently small e{open} the operator H_e{open}(α) has for a.e. α a pure point spectrum. The corresponding eigenfunctions decay exponentially outside a finite set. The integrated density of states is an incomplete devil's staircase with infinitely many flat pieces.

Original language	English (US)
Pages (from-to)	861-909
Number of pages	49
Journal	Journal of Statistical Physics
Volume	46
Issue number	5-6
DOIs	https://doi.org/10.1007/BF01011146
State	Published - Mar 1987

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Green's function
Schrödinger operator
continued fraction
eigenfunction
eigenvalue

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10.1007/BF01011146

Cite this

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title = "Anderson localization for one-dimensional difference Schr{\"o}dinger operator with quasiperiodic potential",

abstract = "The Schr{\"o}dinger difference operator considered here has the form \{Mathematical expression\} where V is a C2-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently small e\{open\} the operator He\{open\}(α) has for a.e. α a pure point spectrum. The corresponding eigenfunctions decay exponentially outside a finite set. The integrated density of states is an incomplete devil's staircase with infinitely many flat pieces.",

keywords = "Green's function, Schr{\"o}dinger operator, continued fraction, eigenfunction, eigenvalue",

author = "Sinai, \{Ya G.\}",

year = "1987",

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pages = "861--909",

journal = "Journal of Statistical Physics",

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T1 - Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential

AU - Sinai, Ya G.

PY - 1987/3

Y1 - 1987/3

N2 - The Schrödinger difference operator considered here has the form {Mathematical expression} where V is a C2-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently small e{open} the operator He{open}(α) has for a.e. α a pure point spectrum. The corresponding eigenfunctions decay exponentially outside a finite set. The integrated density of states is an incomplete devil's staircase with infinitely many flat pieces.

AB - The Schrödinger difference operator considered here has the form {Mathematical expression} where V is a C2-periodic Morse function taking each value at not more than two points. It is shown that for sufficiently small e{open} the operator He{open}(α) has for a.e. α a pure point spectrum. The corresponding eigenfunctions decay exponentially outside a finite set. The integrated density of states is an incomplete devil's staircase with infinitely many flat pieces.

KW - Green's function

KW - Schrödinger operator

KW - continued fraction

KW - eigenfunction

KW - eigenvalue

UR - https://www.scopus.com/pages/publications/0000763917

UR - https://www.scopus.com/pages/publications/0000763917#tab=citedBy

U2 - 10.1007/BF01011146

DO - 10.1007/BF01011146

M3 - Article

AN - SCOPUS:0000763917

SN - 0022-4715

VL - 46

SP - 861

EP - 909

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 5-6

ER -

Anderson localization for one-dimensional difference Schrödinger operator with quasiperiodic potential

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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