Difference equations in the complex plane: quasiclassical asymptotics and Berry phase. Issue 1 (2nd January 2022)

• Record Type: Journal Article
• Authors: Fedotov, Alexander; Shchetka, Ekaterina
• Is Part Of: Applicable analysis. Volume 101:Issue 1(2022)
• Page Start: 274
• Page End: 296
• Publication Date: 2022-01-02
• Subjects: Grigory Panasenko; Difference equation -- complex plane -- quasiclassical asymptotics -- geometric phase; 39A45 -- 81Q20; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1738400
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : We consider the equation Ψ ( z + h ) = M ( z ) Ψ ( z ), where z ∈ C, h >0 is a parameter, and M : C ↦ S L ( 2, C ) is a given analytic function. We get asymptotics of its analytic solutions as h → 0 . The asymptotic formulas contain an analog of the geometric (Berry) phase well known in the quasiclassical analysis of differential equations.