  The inspiration for this theoretical paper comes from recent experiments on a
PT-symmetric system of two coupled optical whispering galleries (optical
resonators). The optical system can be modeled as a pair of coupled linear
oscillators, one with gain and the other with loss. If the coupled oscillators
have a balanced loss and gain, the system is described by a Hamiltonian and the
energy is conserved. This theoretical model exhibits two PT transitions
depending on the size of the coupling parameter \epsilon. For small \epsilon
the PT symmetry is broken and the system is not in equilibrium, but when
\epsilon becomes sufficiently large, the system undergoes a transition to an
equilibrium phase in which the PT symmetry is unbroken. For very large \epsilon
the system undergoes a second transition and is no longer in equilibrium. The
classical and the quantized versions of the system exhibit transitions at
exactly the same values of \epsilon.
