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Title: Non-divergent representation of a non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas
Authors: Hashimoto, Kazunari
Kanki, Kazuki
Hayakawa, Hisao  kyouindb  KAKEN_id
Petrosky, Tomio
Author's alias: 早川, 尚男
Issue Date: Feb-2015
Publisher: Oxford University Press
Journal title: Progress of Theoretical and Experimental Physics
Volume: 2015
Issue: 2
Thesis number: 023A02
Abstract: We propose a non-singular representation for a non-Hermitian operator even if the parameter space contains exceptional points (EPs), at which the operator cannot be diagonalized and the usual spectral representation ceases to exist. Our representation has a generalized Jordan block form and is written in terms of extended pseudo-eigenstates. Our method is free from divergence in the spectral representation at EPs, at which multiple eigenvalues and eigenvectors coalesce and the eigenvectors cannot be normalized. Our representation improves the accuracy of numerical calculations of physical quantities near EPs. We also find that our method is applicable to various problems related to EPs in the parameter space of non-Hermitian operators. We demonstrate the usefulness of our representation by investigating Boltzmann's collision operator in a 1D quantum Lorentz gas in the weak-coupling approximation.
Rights: © The Author(s) 2015. Published by Oxford University Press on behalf of the Physical Society of Japan.
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
DOI(Published Version): 10.1093/ptep/ptu183
Appears in Collections:Journal Articles

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