Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians

A.V. Sokolov

Research output

Abstract

We study intertwining relations for matrix non-Hermitian Hamiltonians by matrix differential first-order and higher-order operators. We show that for any matrix intertwining operator of minimal order there is conjugate (in some sense) matrix intertwining operator such that the products of these operators in different orders are identical polynomials of the corresponding Hamiltonians. The corresponding polynomial algebra of supersymmetry is considered. Theorem on factorization of a matrix differential intertwining operator into product of matrix differential intertwining operators of lower orders with singular, in general, coefficients is proved. The problem of minimization of a matrix differential intertwining operator is considered and criterion of minimizability is presented. The problem of (ir)reducibility of a matrix intertwining operator is considered and criterion of reducibility is proved. It is shown that there are in contrast to the scalar case absolutely irreducible matrix intertwining operators of
Original languageEnglish
Title of host publicationДоклады на международной научной конференции PHHQP XI
PublisherParis Diderot University
Pages1-23
Publication statusPublished - 2012
Externally publishedYes

Fingerprint

Non-Hermitian Matrix
Intertwining Operators
Supersymmetry
Differential operator
Reducibility
Irreducible Matrix
Polynomial Algebra
Operator
Factorization
Scalar
Higher Order
First-order
Polynomial
Coefficient

Cite this

Sokolov, A. V. (2012). Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians. In Доклады на международной научной конференции PHHQP XI (pp. 1-23). Paris Diderot University.
Sokolov, A.V. / Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians. Доклады на международной научной конференции PHHQP XI. Paris Diderot University, 2012. pp. 1-23
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author = "A.V. Sokolov",
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Sokolov, AV 2012, Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians. in Доклады на международной научной конференции PHHQP XI. Paris Diderot University, pp. 1-23.

Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians. / Sokolov, A.V.

Доклады на международной научной конференции PHHQP XI. Paris Diderot University, 2012. p. 1-23.

Research output

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PY - 2012

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N2 - We study intertwining relations for matrix non-Hermitian Hamiltonians by matrix differential first-order and higher-order operators. We show that for any matrix intertwining operator of minimal order there is conjugate (in some sense) matrix intertwining operator such that the products of these operators in different orders are identical polynomials of the corresponding Hamiltonians. The corresponding polynomial algebra of supersymmetry is considered. Theorem on factorization of a matrix differential intertwining operator into product of matrix differential intertwining operators of lower orders with singular, in general, coefficients is proved. The problem of minimization of a matrix differential intertwining operator is considered and criterion of minimizability is presented. The problem of (ir)reducibility of a matrix intertwining operator is considered and criterion of reducibility is proved. It is shown that there are in contrast to the scalar case absolutely irreducible matrix intertwining operators of

AB - We study intertwining relations for matrix non-Hermitian Hamiltonians by matrix differential first-order and higher-order operators. We show that for any matrix intertwining operator of minimal order there is conjugate (in some sense) matrix intertwining operator such that the products of these operators in different orders are identical polynomials of the corresponding Hamiltonians. The corresponding polynomial algebra of supersymmetry is considered. Theorem on factorization of a matrix differential intertwining operator into product of matrix differential intertwining operators of lower orders with singular, in general, coefficients is proved. The problem of minimization of a matrix differential intertwining operator is considered and criterion of minimizability is presented. The problem of (ir)reducibility of a matrix intertwining operator is considered and criterion of reducibility is proved. It is shown that there are in contrast to the scalar case absolutely irreducible matrix intertwining operators of

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KW - matrix intertwining operator

KW - non-Hermitian matrix Hamiltonian

KW - (ir)reducibility

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Sokolov AV. Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians. In Доклады на международной научной конференции PHHQP XI. Paris Diderot University. 2012. p. 1-23