Abstract
The nonHermitian quadratic oscillator known as the Swanson oscillator is one of the popular PTsymmetric model systems. Here a full classical description of its dynamics is derived using recently developed metriplectic flow equations, which combine the classical symplectic flow for Hermitian systems with a dissipative metric flow for the antiHermitian part. Closed form expressions for the metric and phasespace trajectories are presented which are found to be periodic in time. Since the Hamiltonian is only quadratic the classical dynamics exactly describe the quantum dynamics of Gaussian wave packets. It is shown that the classical metric and trajectories as well as the quantum wave functions can diverge in finite time even though the PTsymmetry is unbroken, i.e., the eigenvalues are purely real.
Original language  English 

Article number  055301 
Number of pages  16 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  48 
Issue number  5 
DOIs  
Publication status  Published  16 Jan 2015 
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Dr Roman C V Schubert
 School of Mathematics  Senior Lecturer
 Probability, Analysis and Dynamics
 Mathematical Physics
 Pure Mathematics
Person: Academic , Member