Surprising spectra of PT-symmetric point interactions

TL;DR

This paper investigates the spectral properties of PT-symmetric point interactions in second derivative operators, revealing unusual spectral effects that differ significantly from the self-adjoint case, even with PT-symmetry and related symmetries.

Contribution

It provides a detailed analysis of PT-symmetric point interactions, completing previous results and exploring their spectral effects on finite intervals.

Findings

Spectra of PT-symmetric point interactions differ markedly from self-adjoint cases.

Unusual spectral effects are observed despite PT-symmetry, P-pseudo-Hermiticity, and T-self-adjointness.

The study extends understanding of spectral behavior in non-Hermitian quantum systems.

Abstract

Spectra of the second derivative operators corresponding to the special PT-symmetric point interactions are studied. The results are partly the completion of those obtained in [1]. The particular PT-symmetric point interactions causing unusual spectral effects are investigated for the systems defined on a finite interval as well. The spectrum of this type of interactions is very far from the self-adjoint case despite of PT-symmetry, P-pseudo-Hermiticity and T-self-adjointness.