$${\mathcal {PT}}$$ -symmetric dimers with time-periodic gain/loss function.

$${\mathcal {PT}}$$ -symmetric dimers with a time-periodic gain/loss function in a balanced configuration where the amount of gain equals that of loss are investigated analytically and numerically. Two prototypical dimers in the linear regime are investigated: a system of coupled classical oscillators, and a Schrödinger dimer representing the coupling of field amplitudes, each system representing a wide class of physical models. Through a thorough analysis of their stability behavior, we find that turning on the coupling parameter in the classical dimer system leads initially to decreased stability but then to re-entrant transitions from the exact to the broken $${\mathcal {PT}}$$ -phase and vice versa, as it is increased beyond a critical value. On the other hand, the Schrödinger dimer behaves more like a single oscillator with time-periodic gain/loss. In addition, we are able to identify the conditions under which the behavior of the two dimer systems coincides and/or reduces to that of a single oscillator. [ABSTRACT FROM AUTHOR]