Difference equations in the complex plane: quasiclassical asymptotics and Berry phase. Issue 1 (2nd January 2022) - Fedotov, Alexander; Shchetka, Ekaterina
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.