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<p>For a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{PT}\)</EquationSource> </InlineEquation>-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.</p>

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

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  • 发表日期：

    2025年12月1日

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  • Petr G. Grinevich,
  • Iskander A. Taimanov

摘要

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.