$1/\epsilon$ problem in resurgence. (23rd October 2020)

• Record Type: Journal Article
• Authors: Sueishi, Naohisa
• Is Part Of: Progress of theoretical and experimental physics. Volume 2021:Number 1(2021)
• Publication Date: 2020-10-23
• Subjects: B35 -- B39; Physics -- Periodicals; Mathematical physics -- Periodicals; 530.05
• DOI: 10.1093/ptep/ptaa156
• Languages: English
• ISSNs: 2050-3911

Abstract

Abstract: This paper considers the $1/\epsilon$ problem, which is the divergent behavior of the ground-state energy of the asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and the resurgence technique. Using the resolvent method, it is shown that including not only one complex bion but a multi-complex bion and multi-bounce contributions solves this problem. This result indicates the importance of summing all possible saddle-point contributions and also the relationship between the exact Wentzel–Kramers–Brillouin approximation and path-integral formalism.