PT-symmetry Management in Oligomer Systems

TL;DR

This paper investigates how rapid temporal modulation of gain and loss in PT-symmetric oligomer systems can expand the region of exact PT-symmetry, using averaged equations and theoretical analysis to validate the approach.

Contribution

It introduces a method of PT-symmetry management via rapid modulation and demonstrates its effectiveness through averaged models and comparison with exact solutions.

Findings

Rapid modulation expands the PT-symmetry region.

Averaged models accurately predict time-periodic solutions.

Good agreement between averaged and full non-autonomous models.

Abstract

We study the effects of management of the PT-symmetric part of the potential within the setting of Schr\"odinger dimer and trimer oligomer systems. This is done by rapidly modulating in time the gain/loss profile. This gives rise to a number of interesting properties of the system, which are explored at the level of an averaged equation approach. Remarkably, this rapid modulation provides for a controllable expansion of the region of exact PT-symmetry, depending on the strength and frequency of the imposed modulation. The resulting averaged models are analyzed theoretically and their exact stationary solutions are translated into time-periodic solutions through the averaging reduction. These are, in turn, compared with the exact periodic solutions of the full non-autonomous PT-symmetry managed problem and very good agreement is found between the two.