Transparent boundary conditions for discretized non-Hermitian eigenvalue problems

Jonathan Heinz, Miroslav Kolesik

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A method is presented for transparent, energy-dependent boundary conditions for open, non-Hermitian systems, and is illustrated on an example of Stark resonances in a single-particle quantum system. The approach provides an alternative to external complex scaling, and is applicable when asymptotic solutions can be characterized at large distances from the origin. Its main benefit consists in a drastic reduction of the dimesnionality of the underlying eigenvalue problem. Besides application to quantum mechanics, the method can be used in other contexts such as in systems involving unstable optical cavities and lossy waveguides.

Original languageEnglish (US)
Article number2150138
JournalInternational Journal of Modern Physics C
Issue number10
StatePublished - Oct 1 2021


  • Transparent boundary conditions
  • external scaling
  • metastable states
  • non-hermitian systems
  • open quantum systems
  • stark resonances
  • strong-field ionization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Theory and Mathematics


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