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Transparent boundary conditions for discretized non-Hermitian eigenvalue problems

Author

Listed:
  • Jonathan Heinz

    (James Wyant College of Optical Sciences, University of Arizona, Tucson Arizona 85721, USA)

  • Miroslav Kolesik

    (James Wyant College of Optical Sciences, University of Arizona, Tucson Arizona 85721, USA)

Abstract

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.

Suggested Citation

  • Jonathan Heinz & Miroslav Kolesik, 2021. "Transparent boundary conditions for discretized non-Hermitian eigenvalue problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(10), pages 1-17, October.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:10:n:s0129183121501382
    DOI: 10.1142/S0129183121501382
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