PT-Symmetric Dimer of Coupled Nonlinear Oscillators

Abstract

We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT-symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and anti-symmetric breather solutions, as well as symmetry breaking variants thereof. We propose a reduction of the system to a Schrödinger type PT-symmetric dimer, whose detailed earlier understanding can explain many of the phenomena observed herein, including the PT phase transition. Nevertheless, there are also significant parametric as well as phenomenological potential differences between the two models and we discuss where these arise and where they are most pronounced. Finally, we also provide examples of the evolution dynamics of the different states in their regimes of instability.

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• Nonreciprocal light transmission in parity-time-symmetric whispering-gallery microcavities
• Unidirectional Nonlinear PT-symmetric Optical Structures
• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
• Model of a PT symmetric Bose-Einstein condensate in a delta-functions double well
• Gain-Driven Discrete Breathers in PT-Symmetric Nonlinear Metamaterials
• Twofold Transition in PT-Symmetric Coupled Oscillators
• Discrete solitons in PT-symmetric lattices
• Nonlinear dynamics in PT-symmetric lattices
• Nonlinear PT-symmetric plaquettes

Cited by in corpus (21)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Experimental realization of Floquet PT-symmetric systems
• Coupled Oscillator Systems Having Partial PT Symmetry
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Dimer with gain and loss: Integrability and $\mathcal{P}\mathcal{T}$-symmetry restoration
• Systems of coupled PT-symmetric oscillators
• Jamming anomaly in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear anti-directional couplers with gain and loss
• PT -symmetric rational Calogero model with balanced loss and gain
• PT-symmetry Management in Oligomer Systems
• PT Symmetry, induced mechanical lasing and tunable force sensing in a coupled-mode optically levitated nanoparticle
• PT-symmetric sine-Gordon breathers
• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• On regular and chaotic dynamics of a non-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain
• $\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function
• Exceptional point in a coupled Swanson system
• Systems that become $\mathcal{P}\mathcal{T}$ symmetric through interaction
• Time-dependent spectral renormalization method
• Classical Hamiltonian Systems with Balanced loss and gain
• Complex dynamical properties of coupled Van der Pol-Duffing oscillators with balanced loss and gain