Chaos and $\mathcal{PT}$-symmetry breaking transitions in a driven, nonlinear dimer with balanced gain and loss

TL;DR

This paper explores how a driven, nonlinear $ ext{PT}$-symmetric dimer transitions between regular and chaotic dynamics, revealing the relationship between $ ext{PT}$-symmetry breaking and chaos at different driving frequencies.

Contribution

It demonstrates the connection between $ ext{PT}$-symmetry breaking and chaotic behavior in a driven nonlinear dimer, highlighting frequency-dependent dynamical regimes.

Findings

Regular $ ext{PT}$-symmetric motion at low and high frequencies

Chaotic $ ext{PT}$-symmetry broken states at intermediate frequencies

Interplay between $ ext{PT}$-symmetry breaking and chaos

Abstract

Dynamics of a simple system, such as a two-state (dimer) model, are dramatically changed in the presence of interactions and external driving, and the resultant unitary dynamics show both regular and chaotic regions. We investigate the non-unitary dynamics of such a dimer in the presence of balanced gain and loss for the two states, i.e. a $\mathcal{PT}$ symmetric dimer. We find that at low and high driving frequencies, the $\mathcal{PT}$-symmetric dimer motion continues to be regular, and the system is in the $\mathcal{PT}$-symmetric state. On that other hand, for intermediate driving frequency, the system shows chaotic motion, and is usually in the $\mathcal{PT}$-symmetry broken state. Our results elucidate the interplay between the $\mathcal{PT}$-symmetry breaking transitions and regular-chaotic transitions in an experimentally accessible toy model.