Newton polygons and resonances of multiple delta-potentials

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 -\gam...

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Bibliographic Details
Published in:arXiv.org 2023-08
Main Authors: Datchev, Kiril, Marzuola, Jeremy L, Wunsch, Jared
Format: Article
Language:English
Subjects:
Poles
Polygons
Resonance scattering
Online Access:Get full text
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Summary: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.
ISSN:2331-8422