What question did this study set out to answer?

The aim is to study the bifurcation of the spectrum in one-dimensional Schrödinger operators with periodic potentials when perturbed by PT-symmetric potentials.

June 27, 2026Journal of Inverse and Ill-Posed ProblemsOpen Access

Bifurcation of spectra of periodic self-adjoint operators on axis with small 𝒫𝒯-symmetric potential

View Full Paper

Ask AI

Bookmark

Authors

DBD. I. BorisovPeoples' Friendship University of Russia ITI. A. TaĭmanovNovosibirsk State University

Discussion

Member takes

Implication

Randomized trial investigates the bifurcation of spectrum under PT-symmetric potential perturbation, indicating the emergence of non-real spectra.

Key Points

The aim is to study the bifurcation of the spectrum in one-dimensional Schrödinger operators with periodic potentials when perturbed by PT-symmetric potentials.
Analyzed an even periodic Schrödinger operator with a small PT-symmetric perturbation.
Derived a three-terms asymptotic expansion for perturbed band functions.
Established conditions for the emergence and absence of a non-real spectrum.
Found that the non-real spectrum forms a complex curve, characterized by asymptotic expansions.
Provided rigorous estimates for error terms in the asymptotic expansions.
Described the dependency of Dirichlet eigenvalues on the perturbation in relation to Dubrovin equations.

Cite This Study

Borisov et al. (2026) studied this question.

synapsesocial.com/papers/6a3f67e2aea7db3c1953f251 https://doi.org/10.1515/jiip-2026-0056

View Full Paper

Ask AI

Bookmark

Implication

Randomized trial investigates the bifurcation of spectrum under PT-symmetric potential perturbation, indicating the emergence of non-real spectra.

Bifurcation of spectra of periodic self-adjoint operators on axis with small 𝒫𝒯-symmetric potential

Discussion

Member takes

Implication

Key Points

Cite This Study

Bifurcation of spectra of periodic self-adjoint operators on axis with small 𝒫𝒯-symmetric potential

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider