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Spontaneous PT ‐Symmetry Breaking in Nonlinearly Coupled van der Pol Oscillators
Author(s) -
Jutley Jessica J.,
Aceves Alejandro B.
Publication year - 2016
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12139
Subject(s) - physics , van der pol oscillator , symmetry breaking , nonlinear system , quantum mechanics , quantum , spontaneous symmetry breaking , anharmonicity , context (archaeology) , symmetry (geometry) , explicit symmetry breaking , classical mechanics , quantum electrodynamics , mathematics , paleontology , geometry , biology
Parity‐time ( PT ) symmetry, initially proposed in the context of Quantum Mechanics and Quantum Field Theory, has recently been studied and demonstrated in optical and electronic systems where laboratory demonstrations are possible. The model considered here consists of two nonlinearly coupled van der Pol (VDP) oscillators, originally studied in [1]. This dimer serves as an experimental realization of a class of nonlinear systems, where the anharmonic component has gain for one oscillator and loss of equal strength for the other, so that Hermiticity is broken while PT symmetry is preserved. The existence of spontaneous PT symmetry breaking at some critical value of the gain/loss parameter is proven by use of modulation theory in the weakly nonlinear regime, and by use of asymptotic methods to demonstrate relaxed oscillations for a strongly nonlinear coupling. We then prove similar phenomena in an infinite chain composed of such PT VDP dimers in the long‐wave limit. Finally, we perform initial studies of asymmetric transport properties in the VDP arrays.