Newton polygons and resonances of multiple delta-potentials
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- by Kiril Datchev, Jeremy L. Marzuola and Jared Wunsch;
- Trans. Amer. Math. Soc. 377 (2024), 2009-2025
- DOI: https://doi.org/10.1090/tran/9056
- Published electronically: November 20, 2023
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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 $\operatorname {Im}z \sim -\gamma h \log (1/h).$ 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.References
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Bibliographic Information
- Kiril Datchev
- Affiliation: Mathematics Department, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 860651
- Email: kdatchev@purdue.edu
- Jeremy L. Marzuola
- Affiliation: Mathematics Department, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599
- MR Author ID: 787291
- ORCID: 0000-0002-8668-7143
- Email: marzuola@math.unc.edu
- Jared Wunsch
- Affiliation: Mathematics Department, Northwestern University, Evanston, Illinois 60208
- MR Author ID: 362611
- ORCID: 0000-0001-7466-6858
- Email: jwunsch@math.northwestern.edu
- Received by editor(s): August 31, 2022
- Received by editor(s) in revised form: August 8, 2023
- Published electronically: November 20, 2023
- Additional Notes: The first author was supported from NSF grant DMS-1708511. The second author was supported from NSF grant DMS-1909035. The third author was partially supported by Simons Foundation grant 631302, NSF grant DMS–2054424, and a Simons Fellowship.
- © Copyright 2023 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 377 (2024), 2009-2025
- MSC (2020): Primary 81U24, 35B34
- DOI: https://doi.org/10.1090/tran/9056
- MathSciNet review: 4744748