PT-Symmetric Dimer of Coupled Nonlinear Oscillators

TL;DR

This paper systematically analyzes a PT-symmetric nonlinear oscillator dimer, exploring symmetric and anti-symmetric solutions, symmetry breaking, phase transitions, and dynamic evolution, bridging nonlinear oscillator models with Schrödinger-type dimers.

Contribution

It extends the understanding of PT-symmetric nonlinear oscillators by analyzing both soft and hard nonlinearities and relating them to Schrödinger-type dimers, highlighting differences and dynamic behaviors.

Findings

Identification of symmetric and anti-symmetric breather solutions

Observation of PT phase transition phenomena

Analysis of instability-driven evolution dynamics

Abstract

We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and anti-symmetric breather solutions, as well as symmetry breaking variants thereof. We propose a reduction of the system to a Schr\"odinger type PT-symmetric dimer, whose detailed earlier understanding can explain many of the phenomena observed herein, including the PT phase transition. Nevertheless, there are also significant parametric as well as phenomenological potential differences between the two models and we discuss where these arise and where they are most pronounced. Finally, we also provide examples of the evolution dynamics of the different states in their regimes of instability.