TY - JOUR

T1 - On Perturbations of the Spectrum of a One-Dimensional -Symmetric Periodic Schrödinger Operator

AU - Grinevich, Petr G.

AU - Taimanov, Iskander A.

N1 - The work was supported by RSCF (grant no. 24-11-00281).

PY - 2025/12

Y1 - 2025/12

N2 - For a -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.

AB - For a -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.

KW - PT-symmetry

KW - inverse spectral problem

KW - periodic Schrödinger operator

UR - https://www.scopus.com/pages/publications/105023530360

UR - https://www.mendeley.com/catalogue/d31fc104-6b8b-3aec-9c52-9cff96385838/

U2 - 10.1134/S1560354725060036

DO - 10.1134/S1560354725060036

M3 - Article

VL - 30

SP - 962

EP - 968

JO - Regular and Chaotic Dynamics

JF - Regular and Chaotic Dynamics

SN - 1560-3547

IS - 6

ER -