Imperial College London
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DrEva-MariaGraefe

Faculty of Natural Sciences, Department of Mathematics

Royal Society University Research Fellow (Reader)
 
 
 
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Contact

 

+44 (0)20 7594 8549e.graefe CV

 
 
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Location

 

6M35Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Graefe:2014,
author = {Graefe, E-M and Korsch, HJ and Rush, A and Schubert, R},
journal = {Journal of Physics A-Mathematical and General},
title = {Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator},
url = {http://arxiv.org/abs/1409.6456v1},
year = {2014}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The non-Hermitian quadratic oscillator studied by Swanson is one of thepopular $PT$-symmetric model systems. Here a full classical description of itsdynamics is derived using recently developed metriplectic flow equations, whichcombine the classical symplectic flow for Hermitian systems with a dissipativemetric flow for the anti-Hermitian part. Closed form expressions for the metricand phase-space trajectories are presented which are found to be periodic intime. Since the Hamiltonian is only quadratic the classical dynamics exactlydescribes the quantum dynamics of Gaussian wave packets. It is shown that theclassical metric and trajectories as well as the quantum wave functions candiverge in finite time even though the $PT$-symmetry is unbroken, i.e., theeigenvalues are purely real.
AU  - Graefe,E-M
AU  - Korsch,HJ
AU  - Rush,A
AU  - Schubert,R
PY  - 2014///
SN  - 1361-6447
TI  - Classical and quantum dynamics in the (non-Hermitian) Swanson oscillator
T2  - Journal of Physics A-Mathematical and General
UR  - http://arxiv.org/abs/1409.6456v1
UR  - http://hdl.handle.net/10044/1/19412
ER  -
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