Difference equations in the complex plane: quasiclassical asymptotics and Berry phase

Alexander Fedotov, Ekaterina Shchetka

We study solutions to the difference equation $\Psi (z+h)=M(z)\Psi (z)$ where $z$ is a complex variable, $h>0$ is a parameter, and $M:\mathbb{C}\mapsto SL(2,\mathbb{C})$ is a given analyti…