On Perturbations of the Spectrum of a One-Dimensional \(\mathcal{PT}\)-Symmetric Periodic Schrödinger Operator

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2025-12-01 DOI:10.1134/S1560354725060036

Petr G. Grinevich, Iskander A. Taimanov

引用次数: 0

Abstract

For a \(\mathcal{PT}\)-symmetric periodic Schrödinger 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 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.

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一维\(\mathcal{PT}\) -对称周期Schrödinger算子谱的摄动

对于一个\(\mathcal{PT}\) -对称周期Schrödinger算子，它是零势的一个小扰动，我们计算了扰动理论中阶Bloch函数的谱和零点除数。特别地，我们发现布洛赫光谱的凹痕类似于椭圆，它们的焦点与光谱曲线的分支点重合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.