abstract
The field of PT-symmetric, and more generally non-Hermitian, quantum theory presents exciting possibilities for modelling open systems. However, the dynamics and classical limit of non-Hermitian systems are relatively unexplored. In this talk I will present an exploration of the classical limit and the dynamics of a popular model PT-symmetric system: the non-Hermitian quadratic oscillator known as the Swanson oscillator. I will give a full classical description of its dynamics using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow from the anti-Hermitian part. Since the Hamiltonian is quadratic, the classical dynamics exactly describe the quantum dynamics of Gaussian wave packets. I will show that the classical metric and trajectories, as well as the quantum wave functions, can diverge in finite time even though the PT-symmetry is unbroken, i.e., the eigenvalues are purely real.