Algebraic analysis of non-Hermitian quadratic Hamiltonians

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1. Verfasser: Fernández, Francisco M.
Format: Preprint
Veröffentlicht: 2022
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author Fernández, Francisco M.
author_facet Fernández, Francisco M.
contents We study a general one-mode non-Hermitian quadratic Hamiltonian that does not exhibit $\mathcal{PT}$-symmetry. By means of an algebraic method we determine the conditions for the existence of real eigenvalues as well as the location of the exceptional points. We also put forward an algebraic alternative to the generalized Bogoliubov transformation that enables one to convert the quadratic operator into a simpler form in terms of the original creation and annihilation operators. We carry out a similar analysis of a two-mode oscillator that consists of two identical one-mode oscillators coupled by a quadratic term.
format Preprint
id arxiv_https___arxiv_org_abs_2209_14749
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Algebraic analysis of non-Hermitian quadratic Hamiltonians
Fernández, Francisco M.
Quantum Physics
We study a general one-mode non-Hermitian quadratic Hamiltonian that does not exhibit $\mathcal{PT}$-symmetry. By means of an algebraic method we determine the conditions for the existence of real eigenvalues as well as the location of the exceptional points. We also put forward an algebraic alternative to the generalized Bogoliubov transformation that enables one to convert the quadratic operator into a simpler form in terms of the original creation and annihilation operators. We carry out a similar analysis of a two-mode oscillator that consists of two identical one-mode oscillators coupled by a quadratic term.
title Algebraic analysis of non-Hermitian quadratic Hamiltonians
topic Quantum Physics
url https://arxiv.org/abs/2209.14749