Efficient extraction of resonant states in systems with defects
Numerical Analysis
2023-02-08 v2 Numerical Analysis
Mathematical Physics
math.MP
Abstract
We introduce a new numerical method to compute resonances induced by localized defects in crystals. This method solves an integral equation in the defect region to compute analytic continuations of resolvents. Such an approach enables one to express the resonance in terms of a "resonance source", a function that is strictly localized within the defect region. The kernel of the integral equation, to be applied on such a source term, is the Green function of the perfect crystal, which we show can be computed efficiently by a complex deformation of the Brillouin zone, named Brillouin Complex Deformation (BCD), thereby extending to reciprocal space the concept of complex coordinate transformations.
Cite
@article{arxiv.2204.07063,
title = {Efficient extraction of resonant states in systems with defects},
author = {Ivan Duchemin and Luigi Genovese and Eloïse Letournel and Antoine Levitt and Simon Ruget},
journal= {arXiv preprint arXiv:2204.07063},
year = {2023}
}