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Spectral analysis of the Half-Line Kronig-Penney model with Wigner-Von neumann perturbations. / Lotoreichik, Vladimir; Simonov, Sergey.

In: Reports on Mathematical Physics, Vol. 74, No. 1, 01.08.2014, p. 45-72.

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

Harvard

Lotoreichik, V & Simonov, S 2014, 'Spectral analysis of the Half-Line Kronig-Penney model with Wigner-Von neumann perturbations', Reports on Mathematical Physics, vol. 74, no. 1, pp. 45-72. https://doi.org/10.1016/S0034-4877(14)60057-4

APA

Lotoreichik, V., & Simonov, S. (2014). Spectral analysis of the Half-Line Kronig-Penney model with Wigner-Von neumann perturbations. Reports on Mathematical Physics, 74(1), 45-72. https://doi.org/10.1016/S0034-4877(14)60057-4

Vancouver

Lotoreichik V, Simonov S. Spectral analysis of the Half-Line Kronig-Penney model with Wigner-Von neumann perturbations. Reports on Mathematical Physics. 2014 Aug 1;74(1):45-72. https://doi.org/10.1016/S0034-4877(14)60057-4

Author

Lotoreichik, Vladimir ; Simonov, Sergey. / Spectral analysis of the Half-Line Kronig-Penney model with Wigner-Von neumann perturbations. In: Reports on Mathematical Physics. 2014 ; Vol. 74, No. 1. pp. 45-72.

BibTeX

@article{619843f1a82a4ba3ab36fe16da3f1a9b,
title = "Spectral analysis of the Half-Line Kronig-Penney model with Wigner-Von neumann perturbations",
abstract = "The spectrum of the self-adjoint Schr{\"o}dinger operator associated with the Kronig-Penney model on the half-line has a band-gap structure: its absolutely continuous spectrum consists of intervals (bands) separated by gaps. We show that if one changes strengths of interactions or locations of interaction centers by adding an oscillating and slowly decaying sequence which resembles the classical Wigner-von Neumann potential, then this structure of the absolutely continuous spectrum is preserved. At the same time in each spectral band precisely two critical points appear. At these points {"}instable{"} embedded eigenvalues may exist. We obtain locations of the critical points and discuss for each of them the possibility of an embedded eigenvalue to appear. We also show that the spectrum in gaps remains discrete.",
keywords = "Asymptotic integration, Compact perturbations, Discrete linear systems, Embedded eigenvalues, Kronig-Penney model, Point interactions, Subordinacy theory, Wigner-von Neumann potentials",
author = "Vladimir Lotoreichik and Sergey Simonov",
year = "2014",
month = aug,
day = "1",
doi = "10.1016/S0034-4877(14)60057-4",
language = "English",
volume = "74",
pages = "45--72",
journal = "Reports on Mathematical Physics",
issn = "0034-4877",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Spectral analysis of the Half-Line Kronig-Penney model with Wigner-Von neumann perturbations

AU - Lotoreichik, Vladimir

AU - Simonov, Sergey

PY - 2014/8/1

Y1 - 2014/8/1

N2 - The spectrum of the self-adjoint Schrödinger operator associated with the Kronig-Penney model on the half-line has a band-gap structure: its absolutely continuous spectrum consists of intervals (bands) separated by gaps. We show that if one changes strengths of interactions or locations of interaction centers by adding an oscillating and slowly decaying sequence which resembles the classical Wigner-von Neumann potential, then this structure of the absolutely continuous spectrum is preserved. At the same time in each spectral band precisely two critical points appear. At these points "instable" embedded eigenvalues may exist. We obtain locations of the critical points and discuss for each of them the possibility of an embedded eigenvalue to appear. We also show that the spectrum in gaps remains discrete.

AB - The spectrum of the self-adjoint Schrödinger operator associated with the Kronig-Penney model on the half-line has a band-gap structure: its absolutely continuous spectrum consists of intervals (bands) separated by gaps. We show that if one changes strengths of interactions or locations of interaction centers by adding an oscillating and slowly decaying sequence which resembles the classical Wigner-von Neumann potential, then this structure of the absolutely continuous spectrum is preserved. At the same time in each spectral band precisely two critical points appear. At these points "instable" embedded eigenvalues may exist. We obtain locations of the critical points and discuss for each of them the possibility of an embedded eigenvalue to appear. We also show that the spectrum in gaps remains discrete.

KW - Asymptotic integration

KW - Compact perturbations

KW - Discrete linear systems

KW - Embedded eigenvalues

KW - Kronig-Penney model

KW - Point interactions

KW - Subordinacy theory

KW - Wigner-von Neumann potentials

UR - http://www.scopus.com/inward/record.url?scp=84921944540&partnerID=8YFLogxK

U2 - 10.1016/S0034-4877(14)60057-4

DO - 10.1016/S0034-4877(14)60057-4

M3 - Article

AN - SCOPUS:84921944540

VL - 74

SP - 45

EP - 72

JO - Reports on Mathematical Physics

JF - Reports on Mathematical Physics

SN - 0034-4877

IS - 1

ER -

ID: 9366362