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

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