标题： 关于一维PT对称周期薛定谔算子谱的扰动 显示英文标题

标题： On perturbations of the spectrum of one-dimensional PT-symmetric periodic Schrodinger operator

摘要： 对于PT对称的周期性薛定谔算子，它是零势能的小扰动，我们在微扰理论的领先阶计算谱和布洛赫函数零点的除子。 特别地，我们证明布洛赫谱的间隙的类似物是椭圆，它们的焦点与谱曲线的分支点重合。 显示英文摘要

摘要： For PT-symmetric periodic Schrodinger operator, which is a small perturbation of the zero potential, we calculate the spectrum and the divisor of zeroes of the Bloch function in the leading order of the perturbation theory. In particular, we show that the analogs of lacunae of the Bloch spectrum are ellipses, and their focal points coincide with the branch points of the spectral curve.