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On the absolutely continuous spectrum of one-dimensional quasi-periodic schrödinger operators in the adiabatic limit. / Fedotov, Alexander; Klopp, Frédéric.

в: Transactions of the American Mathematical Society, Том 357, № 11, 01.11.2005, стр. 4481-4516.

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Fedotov, Alexander ; Klopp, Frédéric. / On the absolutely continuous spectrum of one-dimensional quasi-periodic schrödinger operators in the adiabatic limit. в: Transactions of the American Mathematical Society. 2005 ; Том 357, № 11. стр. 4481-4516.

BibTeX

@article{5186cd4e890d4a81a8276a5a866ce46e,
title = "On the absolutely continuous spectrum of one-dimensional quasi-periodic schr{\"o}dinger operators in the adiabatic limit",
abstract = "In this paper we study the spectral properties of families of quasi-periodic Schr{\"o}dinger operators on the real line in the adiabatic limit in the case when the adiabatic iso-energetic curves are extended along the position direction. We prove that, in energy intervals where this is the case, most of the spectrum is purely absolutely continuous in the adiabatic limit, and that the associated generalized eigenfunctions are Bloch-Floquet solutions. R{\'E}SUM{\'E}. Cet article est consacr{\'e} {\`a} l'{\'e}tude du spectre de certaines familles d'{\'e}quations de Schr{\"o}dinger quasi-p{\'e}riodiques sur l'axe r{\'e}el lorsque les vari{\'e}t{\'e} s iso-{\'e}nerg{\'e}tiques adiabatiques sont {\'e}tendues dans la direction des positions. Nous d{\'e}montrons que, dans un intervalle d'{\'e}nergie o{\`u} ceci est le cas, le spectre est dans sa majeure partie purement absolument continu et que les fonctions propres g{\'e}n{\'e}ralis{\'e}es correspondantes sont des fonctions de Bloch-Floquet.",
keywords = "Absolutely continuous spectrum, Adiabatic limit, Bloch-Floquet solutions, Complex WKB method, Monodromy matrix, Quasi-periodic Schr{\"o}dinger equation",
author = "Alexander Fedotov and Fr{\'e}d{\'e}ric Klopp",
year = "2005",
month = nov,
day = "1",
doi = "10.1090/S0002-9947-05-03961-9",
language = "English",
volume = "357",
pages = "4481--4516",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "11",

}

RIS

TY - JOUR

T1 - On the absolutely continuous spectrum of one-dimensional quasi-periodic schrödinger operators in the adiabatic limit

AU - Fedotov, Alexander

AU - Klopp, Frédéric

PY - 2005/11/1

Y1 - 2005/11/1

N2 - In this paper we study the spectral properties of families of quasi-periodic Schrödinger operators on the real line in the adiabatic limit in the case when the adiabatic iso-energetic curves are extended along the position direction. We prove that, in energy intervals where this is the case, most of the spectrum is purely absolutely continuous in the adiabatic limit, and that the associated generalized eigenfunctions are Bloch-Floquet solutions. RÉSUMÉ. Cet article est consacré à l'étude du spectre de certaines familles d'équations de Schrödinger quasi-périodiques sur l'axe réel lorsque les variété s iso-énergétiques adiabatiques sont étendues dans la direction des positions. Nous démontrons que, dans un intervalle d'énergie où ceci est le cas, le spectre est dans sa majeure partie purement absolument continu et que les fonctions propres généralisées correspondantes sont des fonctions de Bloch-Floquet.

AB - In this paper we study the spectral properties of families of quasi-periodic Schrödinger operators on the real line in the adiabatic limit in the case when the adiabatic iso-energetic curves are extended along the position direction. We prove that, in energy intervals where this is the case, most of the spectrum is purely absolutely continuous in the adiabatic limit, and that the associated generalized eigenfunctions are Bloch-Floquet solutions. RÉSUMÉ. Cet article est consacré à l'étude du spectre de certaines familles d'équations de Schrödinger quasi-périodiques sur l'axe réel lorsque les variété s iso-énergétiques adiabatiques sont étendues dans la direction des positions. Nous démontrons que, dans un intervalle d'énergie où ceci est le cas, le spectre est dans sa majeure partie purement absolument continu et que les fonctions propres généralisées correspondantes sont des fonctions de Bloch-Floquet.

KW - Absolutely continuous spectrum

KW - Adiabatic limit

KW - Bloch-Floquet solutions

KW - Complex WKB method

KW - Monodromy matrix

KW - Quasi-periodic Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=27844585359&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-05-03961-9

DO - 10.1090/S0002-9947-05-03961-9

M3 - Article

AN - SCOPUS:27844585359

VL - 357

SP - 4481

EP - 4516

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 11

ER -

ID: 35927840