Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 48, Issue 5, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/48/5/055301
Keywords
quantum dynamics; semiclassical methods; non-Hermitian systems
Categories
Funding
- Imperial College JRF scheme
- L'Oreal UNESCO Women in Science programme
- EPSRC DTA grant
- EPSRC [EP/I019111/1]
- Engineering and Physical Sciences Research Council [1231392, EP/I019111/1] Funding Source: researchfish
- EPSRC [EP/I019111/1] Funding Source: UKRI
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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.
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