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arXiv · 1908.06384

Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials

D. I. Borisov·D. A. Zezyulin
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Abstract

We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large distance. We show that this operator possesses a sequence of approximately equidistant complex-valued wavenumbers situated near the real axis. Depending on its imaginary part, each wavenumber corresponds to either a resonance or an eigenvalue. The obtained sequence of wavenumbers resembles transmission resonances in electromagnetic Fabry-Pérot interferometers formed by parallel mirrors. Our result has potential applications in standard and non-hermitian quantum mechanics, physics of waveguides, photonics, and in other areas where the Schroedinger operator emerges as an effective Hamiltonian.

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D. I. Borisov, D. A. Zezyulin. 2019-09-08. Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials. https://doi.org/10.1016/j.aml.2019.106049

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