期刊
出版社
ROYAL SOC
DOI: 10.1098/rsta.2012.0171
关键词
PT symmetry; oligomer; dynamics
资金
- US National Science Foundation [DMS-0806762]
- Alexander von Humboldt Foundation
- Alexander S. Onassis Public Benefit Foundation
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1000337] Funding Source: National Science Foundation
In the present work, we focus on the cases of two-site (dimer) and three-site (trimer) configurations, i.e. oligomers, respecting the parity-time (PT) symmetry, i.e. with a spatially odd gain-loss profile. We examine different types of solutions of such configurations with linear and nonlinear gain/loss profiles. Solutions beyond the linear PT-symmetry critical point as well as solutions with asymmetric linearization eigenvalues are found in both the nonlinear dimer and trimer. The latter feature is absent in linear PT-symmetric trimers, while both of them are absent in linear PT-symmetric dimers. Furthermore, nonlinear gain/loss terms enable the existence of both symmetric and asymmetric solution profiles (and of bifurcations between them), while only symmetric solutions are present in the linear PT-symmetric dimers and trimers. The linear stability analysis around the obtained solutions is discussed and their dynamical evolution is explored by means of direct numerical simulations. Finally, a brief discussion is also given of recent progress in the context of PT-symmetric quadrimers.
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