Clusters of resonances for a non-selfadjoint multichannel discrete Schrödinger operator

2022/03/02 by Marouane Assal, Assal, Marouane, Olivier Bourget +5 · 1 citation
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.2203.01352

Abstract

We study the distribution of resonances for discrete Hamiltonians of the form H₀+V near the thresholds of the spectrum of H₀. Here, the unperturbed operator H₀ is a multichannel Laplace type operator on ℓ²(\mathbb Z; \mathbb C^N) ≅ ℓ²(\mathbb Z)⊗ \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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