Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials
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-P\'erot 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.
Cite
@article{arxiv.1908.06384,
title = {Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials},
author = {D. I. Borisov and D. A. Zezyulin},
journal= {arXiv preprint arXiv:1908.06384},
year = {2019}
}