Revisiting the PT -symmetric trimer: Bifurcations, ghost states and associated dynamics

Publication date
2013-09
Document type
Research article
Author
Li, Kai
Kevrekidis, Panayotis G.
Frantzeskakis, Dimitri J.
Rüter, Christian E.
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DOI
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ISSN
Series or journal
Journal of physics : concerned with the fundamental mathematical and computational methods underpinning physics, the journal is particularly relevant to statistical physics, chaotic and complex systems, classical and quantum mechanics and classical and quantum field theory. A, Mathematical and theoretical
Periodical volume
46
Part of the university bibliography
✅
Abstract
In this paper, we revisit one of the prototypical PT -symmetric oligomers, namely the trimer. We find all the relevant branches of regular solutions and analyze the bifurcations and instabilities thereof. Our work generalizes the formulation that was recently proposed in the case of dimers for the so-called ghost states of trimers, which we also identify and connect to symmetrybreaking bifurcations from the regular states. We also examine the dynamics of unstable trimers, as well as those of the ghost states in the parametric regime where the latter are found to exist. Finally, we present the current state-of-theart for optical experiments in PT -symmetric trimers, as well as experimental results in a gainlossgain three channel waveguide structure. © 2013 IOP Publishing Ltd.
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