Resurgent Analysis of the Witten Laplacian in One Dimension
Alexander Getmanenko
TL;DR
This paper investigates the low-lying eigenvalues of the Witten Laplacian on the circle using complex WKB and resurgent analysis, revealing their resurgent nature under specific conditions.
Contribution
It introduces a resurgent analysis approach to the Witten Laplacian on the circle, providing new insights into its eigenvalues.
Findings
Low-lying eigenvalues are shown to be resurgent.
Resurgent analysis applies under certain assumptions.
Method bridges complex WKB and spectral analysis.
Abstract
The Witten Laplacian corresponding to a Morse function on the circle is studied using methods of complex WKB and resurgent analysis. It is shown that under certain assumptions the low-lying eigenvalues of the Witten Laplacian are resurgent.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Quantum Mechanics and Non-Hermitian Physics · Magnetism in coordination complexes