### Abstract

Original language | English |
---|---|

Title of host publication | Доклады на международной научной конференции PHHQP XI |

Publisher | Paris Diderot University |

Pages | 1-23 |

Publication status | Published - 2012 |

Externally published | Yes |

### Fingerprint

### Cite this

*Доклады на международной научной конференции PHHQP XI*(pp. 1-23). Paris Diderot University.

}

*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.

Research output

TY - GEN

T1 - Linear and Non-linear Supersymmetry for Non-Hermitian Matrix Hamiltonians

AU - Sokolov, A.V.

PY - 2012

Y1 - 2012

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

KW - Supersymmetry

KW - matrix intertwining operator

KW - non-Hermitian matrix Hamiltonian

KW - (ir)reducibility

M3 - Conference contribution

SP - 1

EP - 23

BT - Доклады на международной научной конференции PHHQP XI

PB - Paris Diderot University

ER -