PT-symmetric dimer as a Hamiltonian system

What is it about?

We show that 2 nonlinear oscillators, one with loss, other with gain, can couple to form a conservative system. Although this system is nonlinear, it admits simple explicit solutions. The nonlinearity protects this system from blowing up: even if the gain and loss are extremely intense, stable stationary and periodic states with large enough amplitudes continue to exist.

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Why is it important?

This system has 3 unusual properties, one mathematical and two physical. First, it admits exact solutions -- as if it were a linear system -- despite being very nonlinear. Second, it is conservative despite having channels for gaining and losing energy. Third, no matter how strong is the pumping of energy into the system and how intense is the dissipation, the system exhibits stable stationary and periodic regimes. The nonlinearity serves as a protector of regularity and order in this system.