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arXiv · 2203.01352

Clusters of resonances for a non-selfadjoint multichannel discrete Schr\"odinger operator

Marouane Assal·Olivier Bourget·Pablo Miranda·Diomba Sambou
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Abstract

We study the distribution of resonances for discrete Hamiltonians of the form $H_0+V$ near the thresholds of the spectrum of $H_0$. Here, the unperturbed operator $H_0$ is a multichannel Laplace type operator on $\ell^2(\mathbb Z; \mathbb C^N) \cong \ell^2(\mathbb Z)\otimes \mathbb C^N$ and $V$ is a non-selfadjoint compact perturbation. We compute the exact number of resonances and give a precise description on their location in clusters around some special points in the complex plane.

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Marouane Assal, Olivier Bourget, Pablo Miranda, Diomba Sambou. 2022-03-02. Clusters of resonances for a non-selfadjoint multichannel discrete Schr\"odinger operator. https://doi.org/10.1063/5.0257944

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