Newton polygons and resonances of multiple delta-potentials

Kiril Datchev; Jeremy L. Marzuola; Jared Wunsch

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arXiv · 2208.07901

Newton polygons and resonances of multiple delta-potentials

Kiril Datchev·Jeremy L. Marzuola·Jared Wunsch

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Abstract

We prove explicit asymptotics for the location of semiclassical scattering resonances in the setting of $h$-dependent delta-function potentials on $\mathbb{R}$. In the cases of two or three delta poles, we are able to show that resonances occur along specific lines of the form $\Im z \sim -\gamma h \log(1/h).$ More generally, we use the method of Newton polygons to show that resonances near the real axis may only occur along a finite collection of such lines, and we bound the possible number of values of the parameter $\gamma.$ We present numerical evidence of the existence of more and more possible values of $\gamma$ for larger numbers of delta poles.

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Kiril Datchev, Jeremy L. Marzuola, Jared Wunsch. 2022-08-16. Newton polygons and resonances of multiple delta-potentials. https://arxiv.org/abs/2208.07901

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