Superoscillatory PT-symmetric potentials

TL;DR

This paper explores PT-symmetric quantum potentials based on superoscillatory functions, revealing complex symmetry-breaking transitions and the potential for restoring PT symmetry through parameter adjustments.

Contribution

It introduces a novel class of PT-symmetric potentials using superoscillatory functions and analyzes their unique symmetry-breaking behaviors and restoration possibilities.

Findings

Suboscillatory potentials yield real eigenvalues.

Superoscillatory potentials exhibit intricate PT-symmetry-breaking transitions.

PT symmetry can be restored by tuning parameters.

Abstract

We introduce the one-dimensional PT-symmetric Schrodinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatory-like potential always generates an entirely real eigenvalue spectrum, its counterpart based on the superoscillatory wave function gives rise to an intricate pattern of PT-symmetry-breaking transitions, controlled by the parameters of the superoscillatory function. One scenario of the transitions proceeds smoothly via a set of threshold values, while another one exhibits a sudden jump to the broken PT symmetry. Another noteworthy finding is the possibility of restoration of the PT symmetry, following its original loss, in the course of the variation of the parameters.