MISC

2015年2月

Non-divergent representation of a non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS
  • Kazunari Hashimoto
  • ,
  • Kazuki Kanki
  • ,
  • Hisao Hayakawa
  • ,
  • Tomio Petrosky

2
記述言語
英語
掲載種別
機関テクニカルレポート,技術報告書,プレプリント等
DOI
10.1093/ptep/ptu183
出版者・発行元
OXFORD UNIV PRESS INC

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.

リンク情報
DOI
https://doi.org/10.1093/ptep/ptu183
arXiv
http://arxiv.org/abs/arXiv:1409.7453
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000351521200006&DestApp=WOS_CPL
URL
http://arxiv.org/abs/1409.7453v3
ID情報
  • DOI : 10.1093/ptep/ptu183
  • ISSN : 2050-3911
  • arXiv ID : arXiv:1409.7453
  • Web of Science ID : WOS:000351521200006

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