Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator

Eva-Maria Graefe, Hans Jürgen Korsch, Alexander Rush, Roman Schubert

Research output: Contribution to journalArticle (Academic Journal)peer-review

17 Citations (Scopus)
236 Downloads (Pure)


The non-Hermitian quadratic oscillator known as the Swanson oscillator is one of the popular PT-symmetric 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 anti-Hermitian part. Closed form expressions for the metric and phase-space 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 PT-symmetry is unbroken, i.e., the eigenvalues are purely real.
Original languageEnglish
Article number055301
Number of pages16
JournalJournal of Physics A: Mathematical and Theoretical
Issue number5
Publication statusPublished - 16 Jan 2015

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