2024/10/12 by Tatsuhiro Misumi, Misumi, Tatsuhiro, Cihan Pazarbaşı +1 · 1 citation
Chemistry · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Gyrotron and Vacuum Electronics Research #High Energy Physics - Theory (hep-th) #Inorganic Fluorides and Related Compounds #Mathematical Physics (math-ph) #Organic and Molecular Conductors Research #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2410.09511
openalex publication_date 2024/10/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore the exact-WKB (EWKB) method through the analysis of Airy and Weber types, with an emphasis on the exact quantization of locally harmonic potentials in multiple sectors. The core innovation of our work lies in introducing a novel complexification approach to the energy parameter u, distinct from the common complexification of the (semi-classical) expansion parameter used in Borel summability. This new technique allows for continuous analytical continuation across different sectors of a potential while maintaining the exact quantization condition, even before median summation. By redefining the A-cycle above the potential barrier top, we ensure the quantization condition remains real and, by use of the Stokes automorphism and the median resummation, show that the resurgence structure is preserved across transitions between sectors. Furthermore, we discuss the Weber-type exact-WKB method, offering exact estimates for quantum actions around all types of saddle points, generalizing previous results. Through the analysis of these quantum actions, we reveal the presence of S-duality, facilitating the exchange between perturbative and non-perturbative behaviors, and we conjecture the mapping of the P-NP relations between dual theories. Our study encompasses periodic and symmetric double-well potentials, demonstrating that the exact-WKB method captures intricate structures in quantum systems in all sectors, including multi-instanton contributions and the resurgence of quantum actions.