Loss, gain, and singular points in open quantum systems
type: Item
instance of: scholarly article
title: Loss, gain, and singular points in open quantum systems
zbMATH Open document ID: 1404.81147
DOI: 10.1155/2018/3653851
author: H. Eleuch
author: I. Rotter
published in: Advances in Mathematical Physics
publication date: 2018-12-11T00:00:00Z
review text: Summary: Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues \(\mathcal{E}_i \equiv E_i + i \Gamma_i / 2\) of the non-Hermitian Hamiltonian \(\mathcal{H}\) coalesce (where \(E_i\) is the energy and \(\Gamma_i\) is the inverse lifetime of the state \(i\)). We show that also the eigenfunctions \(\Phi_i\) of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points \(a = a^{\text{cr}}\) in the parameter space, the biorthogonal eigenfunctions of \(\mathcal{H}\) become orthogonal. For illustration, we show characteristic numerical results.
Mathematics Subject Classification ID: 81S22
Mathematics Subject Classification ID: 81Q12
Mathematics Subject Classification ID: 81P16
zbMATH DE Number: 6991952
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3653851
OpenAlex ID: W2889092637
cites work: Q5526485
cites work: Non-Hermitian Quantum Mechanics
cites work: A non-Hermitian Hamilton operator and the physics of open quantum systems
cites work: Avoided level crossings in open quantum systems
cites work: Exceptional points for logic operations at the molecular level
Wikidata QID: Q129291860
description: scientific article; zbMATH DE number 6991952