Observation of PT phase transition in a simple mechanical system

If a quantum-mechanical Hamiltonian is PT symmetric, there are two possibilities: either all of the eigenvalues are real, in which case the Hamiltonian is said to be in an unbroken-PT-symmetric phase, or else some of the eigenvalues are real and some are complex, in which case the Hamiltonian is said to be in a broken-PT-symmetric phase. As one varies the parameters of the Hamiltonian, one can pass through the phase transition that separates the unbroken and broken phases. This transition has recently been observed in a variety of laboratory experiments. This paper explains the phase transition in a simple and intuitive fashion and then describes an elementary experiment in which the phase transition is easily observed.