Transparent boundary conditions for discretized non-Hermitian eigenvalue problems

Jonathan Heinz and Miroslav Kolesik ()
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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

International Journal of Modern Physics C (IJMPC), 2021, vol. 32, issue 10, 1-17

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.

Keywords: Transparent boundary conditions; metastable states; stark resonances; strong-field ionization; external scaling; non-hermitian systems; open quantum systems (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0129183121501382

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