Standard

Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians : I. General properties. / Andrianov, A. A.; Cannata, F.; Sokolov, A. V.

In: Nuclear Physics B, Vol. 773, No. 3, 02.07.2007, p. 107-136.

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

Harvard

Andrianov, AA, Cannata, F & Sokolov, AV 2007, 'Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties', Nuclear Physics B, vol. 773, no. 3, pp. 107-136. https://doi.org/10.1016/j.nuclphysb.2007.03.016

APA

Andrianov, A. A., Cannata, F., & Sokolov, A. V. (2007). Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties. Nuclear Physics B, 773(3), 107-136. https://doi.org/10.1016/j.nuclphysb.2007.03.016

Vancouver

Andrianov AA, Cannata F, Sokolov AV. Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties. Nuclear Physics B. 2007 Jul 2;773(3):107-136. https://doi.org/10.1016/j.nuclphysb.2007.03.016

Author

Andrianov, A. A. ; Cannata, F. ; Sokolov, A. V. / Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians : I. General properties. In: Nuclear Physics B. 2007 ; Vol. 773, No. 3. pp. 107-136.

BibTeX

@article{a0688f721bbb47a68a638e85c157fb9c,
title = "Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties",
abstract = "We study complex potentials and related non-diagonalizable Hamiltonians with special emphasis on formal definitions of associated functions and Jordan cells. The non-linear SUSY for complex potentials is considered and the theorems characterizing its structure are presented. We define the class of complex potentials invariant under SUSY transformations for (non-)diagonalizable Hamiltonians and formulate several results concerning the properties of associated functions. We comment on the applicability of these results for softly non-Hermitian PT-symmetric Hamiltonians. The role of SUSY (Darboux) transformations in increasing/decreasing of Jordan cells in SUSY partner Hamiltonians is thoroughly analyzed and summarized in the Index Theorem. The properties of non-diagonalizable Hamiltonians as well as the Index Theorem are illustrated in the solvable examples of non-Hermitian reflectionless Hamiltonians. The rigorous proofs are relegated to part II of this paper. At last, some peculiarities in resolution of identity for discrete and continuous spectra with a zero-energy bound state at threshold are discussed.",
author = "Andrianov, {A. A.} and F. Cannata and Sokolov, {A. V.}",
year = "2007",
month = jul,
day = "2",
doi = "10.1016/j.nuclphysb.2007.03.016",
language = "English",
volume = "773",
pages = "107--136",
journal = "Nuclear Physics B",
issn = "0550-3213",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - Non-linear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians

T2 - I. General properties

AU - Andrianov, A. A.

AU - Cannata, F.

AU - Sokolov, A. V.

PY - 2007/7/2

Y1 - 2007/7/2

N2 - We study complex potentials and related non-diagonalizable Hamiltonians with special emphasis on formal definitions of associated functions and Jordan cells. The non-linear SUSY for complex potentials is considered and the theorems characterizing its structure are presented. We define the class of complex potentials invariant under SUSY transformations for (non-)diagonalizable Hamiltonians and formulate several results concerning the properties of associated functions. We comment on the applicability of these results for softly non-Hermitian PT-symmetric Hamiltonians. The role of SUSY (Darboux) transformations in increasing/decreasing of Jordan cells in SUSY partner Hamiltonians is thoroughly analyzed and summarized in the Index Theorem. The properties of non-diagonalizable Hamiltonians as well as the Index Theorem are illustrated in the solvable examples of non-Hermitian reflectionless Hamiltonians. The rigorous proofs are relegated to part II of this paper. At last, some peculiarities in resolution of identity for discrete and continuous spectra with a zero-energy bound state at threshold are discussed.

AB - We study complex potentials and related non-diagonalizable Hamiltonians with special emphasis on formal definitions of associated functions and Jordan cells. The non-linear SUSY for complex potentials is considered and the theorems characterizing its structure are presented. We define the class of complex potentials invariant under SUSY transformations for (non-)diagonalizable Hamiltonians and formulate several results concerning the properties of associated functions. We comment on the applicability of these results for softly non-Hermitian PT-symmetric Hamiltonians. The role of SUSY (Darboux) transformations in increasing/decreasing of Jordan cells in SUSY partner Hamiltonians is thoroughly analyzed and summarized in the Index Theorem. The properties of non-diagonalizable Hamiltonians as well as the Index Theorem are illustrated in the solvable examples of non-Hermitian reflectionless Hamiltonians. The rigorous proofs are relegated to part II of this paper. At last, some peculiarities in resolution of identity for discrete and continuous spectra with a zero-energy bound state at threshold are discussed.

UR - http://www.scopus.com/inward/record.url?scp=34248594954&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2007.03.016

DO - 10.1016/j.nuclphysb.2007.03.016

M3 - Article

AN - SCOPUS:34248594954

VL - 773

SP - 107

EP - 136

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -

ID: 36468994