Year: 2018
Type: article
Abstract: We introduce the one-dimensional $\mathcal{PT}$-symmetric Schr\"odinger equation, with complex potentials in the form of the canonical superoscillatory and suboscillatory functions known in quantum mechanics and optics. While the suboscillatorylike potential always generates an entirely real eigenvalue spectrum, its counterpart based on the superoscillatory wave function gives rise to an intricate pattern of $\mathcal{PT}$-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 $\mathcal{PT}$ symmetry. Another noteworthy finding is the possibility of restoration of the $\mathcal{PT}$ symmetry, following its original loss, in the course of the variation of the parameters.
Source: Physical Review A
Authors: Yaniv Eliezer, Alon Bahabad, Boris A. Malomed
Institution: Tel Aviv University
Language: Latvian
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951325415