Systems of coupled PT-symmetric oscillators

The Hamiltonian for a PT-symmetric chain of coupled oscillators is constructed. It is shown that if the loss-gain parameter gamma is uniform for all oscillators, then as the number of oscillators increases, the region of unbroken PT symmetry disappears entirely. However, if gamma is localized in the sense that it decreases for more distant oscillators, then the unbroken PT-symmetric region persists even as the number of oscillators approaches infinity. In the continuum limit the oscillator system is described by a PT-symmetric pair of wave equations, and a localized loss-gain impurity leads to a pseudobound state. It is also shown that a planar configuration of coupled oscillators can have multiple disconnected regions of unbroken PT symmetry.