Standard

Resolutions of identity for some non-Hermitian Hamiltonians. I. exceptional point in continuous spectrum. / Andrianov, Alexander A.; Sokolov, Andrey V.

In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 7, 111, 05.12.2011.

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

Harvard

Andrianov, AA & Sokolov, AV 2011, 'Resolutions of identity for some non-Hermitian Hamiltonians. I. exceptional point in continuous spectrum', Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 7, 111. https://doi.org/10.3842/SIGMA.2011.111

APA

Andrianov, A. A., & Sokolov, A. V. (2011). Resolutions of identity for some non-Hermitian Hamiltonians. I. exceptional point in continuous spectrum. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7, [111]. https://doi.org/10.3842/SIGMA.2011.111

Vancouver

Andrianov AA, Sokolov AV. Resolutions of identity for some non-Hermitian Hamiltonians. I. exceptional point in continuous spectrum. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2011 Dec 5;7. 111. https://doi.org/10.3842/SIGMA.2011.111

Author

Andrianov, Alexander A. ; Sokolov, Andrey V. / Resolutions of identity for some non-Hermitian Hamiltonians. I. exceptional point in continuous spectrum. In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). 2011 ; Vol. 7.

BibTeX

@article{480ee3da81534fa3836aa6a112c3f882,
title = "Resolutions of identity for some non-Hermitian Hamiltonians. I. exceptional point in continuous spectrum",
abstract = "Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration possess the continuous spectrum and the following peculiarities are investigated: (1) the case when there is an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum; (2) the case when there is an exceptional point situated inside of continuous spectrum. The reductions of the derived resolutions of identity under narrowing of the classes of employed test functions are revealed. It is shown that in the case (1) some of associated functions included into the resolution of identity are normalizable and some of them may be not and in the case (2) the bounded associated function corresponding to the exceptional point does not belong to the physical state space. Spectral properties of a SUSY partner Hamiltonian for the Hamiltonian with an exceptional point are examined.",
keywords = "Exceptional points, Non-Hermitian quantum mechanics, Resolution of identity, Supersymmetry",
author = "Andrianov, {Alexander A.} and Sokolov, {Andrey V.}",
year = "2011",
month = dec,
day = "5",
doi = "10.3842/SIGMA.2011.111",
language = "English",
volume = "7",
journal = "Symmetry, Integrability and Geometry - Methods and Applications",
issn = "1815-0659",
publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

RIS

TY - JOUR

T1 - Resolutions of identity for some non-Hermitian Hamiltonians. I. exceptional point in continuous spectrum

AU - Andrianov, Alexander A.

AU - Sokolov, Andrey V.

PY - 2011/12/5

Y1 - 2011/12/5

N2 - Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration possess the continuous spectrum and the following peculiarities are investigated: (1) the case when there is an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum; (2) the case when there is an exceptional point situated inside of continuous spectrum. The reductions of the derived resolutions of identity under narrowing of the classes of employed test functions are revealed. It is shown that in the case (1) some of associated functions included into the resolution of identity are normalizable and some of them may be not and in the case (2) the bounded associated function corresponding to the exceptional point does not belong to the physical state space. Spectral properties of a SUSY partner Hamiltonian for the Hamiltonian with an exceptional point are examined.

AB - Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration possess the continuous spectrum and the following peculiarities are investigated: (1) the case when there is an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum; (2) the case when there is an exceptional point situated inside of continuous spectrum. The reductions of the derived resolutions of identity under narrowing of the classes of employed test functions are revealed. It is shown that in the case (1) some of associated functions included into the resolution of identity are normalizable and some of them may be not and in the case (2) the bounded associated function corresponding to the exceptional point does not belong to the physical state space. Spectral properties of a SUSY partner Hamiltonian for the Hamiltonian with an exceptional point are examined.

KW - Exceptional points

KW - Non-Hermitian quantum mechanics

KW - Resolution of identity

KW - Supersymmetry

UR - http://www.scopus.com/inward/record.url?scp=84857187942&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2011.111

DO - 10.3842/SIGMA.2011.111

M3 - Article

AN - SCOPUS:84857187942

VL - 7

JO - Symmetry, Integrability and Geometry - Methods and Applications

JF - Symmetry, Integrability and Geometry - Methods and Applications

SN - 1815-0659

M1 - 111

ER -

ID: 98658460