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Linear and nonlinear parity-time-symmetric oligomers: a dynamical systems analysis.
1Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA.
Nonlinear parity-time (PT) symmetric dimers and trimers exhibit unique solutions, including asymmetric ones, beyond linear PT-symmetry limits. These nonlinear systems allow for both symmetric and asymmetric solution profiles, unlike their linear counterparts.
Area of Science:
- Nonlinear physics
- Quantum mechanics
- Optics
Background:
- Parity-time (PT) symmetry in physical systems offers unique properties.
- Oligomeric configurations (dimers, trimers) are fundamental structures in PT-symmetric studies.
- Linear PT-symmetric systems have limitations in solution diversity.
Purpose of the Study:
- To investigate solutions in two-site (dimer) and three-site (trimer) configurations respecting PT symmetry.
- To explore the impact of nonlinear gain/loss profiles on PT-symmetric oligomers.
- To compare solutions in linear versus nonlinear PT-symmetric dimers and trimers.
Main Methods:
- Analysis of linear and nonlinear gain/loss profiles in PT-symmetric systems.
- Examination of dimer and trimer configurations.
- Linear stability analysis and direct numerical simulations for dynamical evolution.
Main Results:
- Nonlinear PT-symmetric dimers and trimers yield solutions beyond the linear critical point.
- Asymmetric linearization eigenvalues are found in nonlinear dimers and trimers, unlike linear cases.
- Nonlinear terms permit both symmetric and asymmetric solution profiles and bifurcations.
Conclusions:
- Nonlinear gain/loss terms significantly expand the solution space in PT-symmetric oligomers.
- The study highlights the richer dynamics and solution landscape of nonlinear PT-symmetric systems.
- Findings pave the way for exploring more complex PT-symmetric structures like quadrimers.
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