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A complex WKB method for adiabatic problems. / Fedotov, Alexander; Klopp, Frédéric.

In: Asymptotic Analysis, Vol. 27, No. 3-4, 01.09.2001, p. 219-264.

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

Harvard

Fedotov, A & Klopp, F 2001, 'A complex WKB method for adiabatic problems', Asymptotic Analysis, vol. 27, no. 3-4, pp. 219-264.

APA

Fedotov, A., & Klopp, F. (2001). A complex WKB method for adiabatic problems. Asymptotic Analysis, 27(3-4), 219-264.

Vancouver

Fedotov A, Klopp F. A complex WKB method for adiabatic problems. Asymptotic Analysis. 2001 Sep 1;27(3-4):219-264.

Author

Fedotov, Alexander ; Klopp, Frédéric. / A complex WKB method for adiabatic problems. In: Asymptotic Analysis. 2001 ; Vol. 27, No. 3-4. pp. 219-264.

BibTeX

@article{c88769d8d330468aba663adca78d66b2,
title = "A complex WKB method for adiabatic problems",
abstract = "This work is devoted to a new version of the complex WKB method suited for adiabatic perturbations of one-dimensional periodic Schr{\"o}dinger operators. Therefore, we introduce an additional parameter, and it is this parameter (and not the variable of the equation) that will become complex. This naturally leads to canonical domains where we construct solutions of the Schr{\"o}dinger equation with a standard asymptotic behavior. These can be used to compute the asymptotics of the exponentially small coefficients of transfer matrices (e.g., scattering matrices, monodromy matrices, etc.). We give an example of such a computation.",
keywords = "Adiabatic perturbations, Complex WKB method, Periodic Schr{\"o}dinger equation",
author = "Alexander Fedotov and Fr{\'e}d{\'e}ric Klopp",
year = "2001",
month = sep,
day = "1",
language = "English",
volume = "27",
pages = "219--264",
journal = "Asymptotic Analysis",
issn = "0921-7134",
publisher = "IOS Press",
number = "3-4",

}

RIS

TY - JOUR

T1 - A complex WKB method for adiabatic problems

AU - Fedotov, Alexander

AU - Klopp, Frédéric

PY - 2001/9/1

Y1 - 2001/9/1

N2 - This work is devoted to a new version of the complex WKB method suited for adiabatic perturbations of one-dimensional periodic Schrödinger operators. Therefore, we introduce an additional parameter, and it is this parameter (and not the variable of the equation) that will become complex. This naturally leads to canonical domains where we construct solutions of the Schrödinger equation with a standard asymptotic behavior. These can be used to compute the asymptotics of the exponentially small coefficients of transfer matrices (e.g., scattering matrices, monodromy matrices, etc.). We give an example of such a computation.

AB - This work is devoted to a new version of the complex WKB method suited for adiabatic perturbations of one-dimensional periodic Schrödinger operators. Therefore, we introduce an additional parameter, and it is this parameter (and not the variable of the equation) that will become complex. This naturally leads to canonical domains where we construct solutions of the Schrödinger equation with a standard asymptotic behavior. These can be used to compute the asymptotics of the exponentially small coefficients of transfer matrices (e.g., scattering matrices, monodromy matrices, etc.). We give an example of such a computation.

KW - Adiabatic perturbations

KW - Complex WKB method

KW - Periodic Schrödinger equation

UR - http://www.scopus.com/inward/record.url?scp=0035446787&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035446787

VL - 27

SP - 219

EP - 264

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 3-4

ER -

ID: 35928194