复平面上的差分方程：拟经典渐近性与Berry相
Difference equations in the complex plane: quasiclassical asymptotics and Berry phase
摘要：
研究了差分方程$Ψ(z+h)=M(z)Ψ(z)$的解，其中$z$是复变，$h>0$是参数，$M:\mathbb{C}\mapsto SL(2,\mathbb{C})$是给定的解析函数.我们将其解析解的渐近性描述为$h\to 0$。渐近公式包含一个模拟的几何（贝里）相位众所周知的准经典分析微分方程。
英文摘要：
We study solutions to the difference equation $Ψ(z+h)=M(z)Ψ(z)$ where $z$ is a complex variable, $h>0$ is a parameter, and $M:\mathbb{C}\mapsto SL(2,\mathbb{C})$ is a given analytic function. We describe the asymptotics of its analytic solutions as $h\to 0$. The asymptotic formulas contain an analog of the geometric (Berry) phase well-known in the quasiclassical analysis of differential equations.
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