Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis
Davide Masoero, Vera De Benedetti
TL;DR
This paper demonstrates that the poles of integrale tritronquee asymptotically align with solutions of Bohr-Sommerfeld quantization conditions, revealing a deep connection between complex analysis and quantum oscillators.
Contribution
It establishes the asymptotic localization of poles of integrale tritronquee near solutions of the Bohr-Sommerfeld-Boutroux system using WKB analysis.
Findings
Poles are asymptotically close to Bohr-Sommerfeld-Boutroux solutions.
The distance between poles and quantization solutions vanishes asymptotically.
Provides a link between complex poles and quantum quantization conditions.
Abstract
Poles of integrale tritronquee are in bijection with cubic oscillators that admit the simultaneous solutions of two quantization conditions. We show that the poles lie near the solutions of a pair of Bohr-Sommerfeld quantization conditions (the Bohr-Sommerfeld-Boutroux system): the distance between a pole and the corresponding solution of the Bohr-Sommerfeld-Boutroux system vanishes asymptotically.
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