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

A.V. Sokolov

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучная

Выдержка

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
Язык оригиналаанглийский
Название основной публикацииДоклады на международной научной конференции PHHQP XI
ИздательParis Diderot University
Страницы1-23
СостояниеОпубликовано - 2012
Опубликовано для внешнего пользованияДа

Отпечаток

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

Цитировать

Sokolov, A. V. (2012). Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians. В Доклады на международной научной конференции PHHQP XI (стр. 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. стр. 1-23
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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",
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author = "A.V. Sokolov",
year = "2012",
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booktitle = "Доклады на международной научной конференции PHHQP XI",
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Sokolov, AV 2012, Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians. в Доклады на международной научной конференции PHHQP XI. Paris Diderot University, стр. 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. стр. 1-23.

Результат исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучная

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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

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