Integrable oscillator type and Schrödinger type dimers

DOI10.1088/1751-8121/aa5362zbMath1357.81112OpenAlexW2569293979MaRDI QIDQ2965737

Avadh Saxena, Avinash Khare

Publication date: 3 March 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/1751-8121/aa5362

zbMATH Keywords

PT-symmetryconstants of motionnonlinear oscillatorStokes variables

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (6)

Integrability and trajectory confinement in -symmetric waveguide arrays ⋮ Complex dynamical properties of coupled Van der Pol–Duffing oscillators with balanced loss and gain ⋮ Taming Hamiltonian systems with balanced loss and gain via Lorentz interaction: general results and a case study with Landau Hamiltonian ⋮ Balanced loss-gain induced chaos in a periodic Toda lattice ⋮ Integrable coupled Liénard-type systems with balanced loss and gain ⋮ On regular and chaotic dynamics of a non- PT -symmetric Hamiltonian system of a coupled Duffing oscillator with balanced loss and gain

Cites Work

• \({\mathcal{PT}}\)-symmetric periodic optical potentials
• \(\mathcal{PT}\)-symmetric dimer in a generalized model of coupled nonlinear oscillators
• Integrable and superintegrable Hamiltonian systems in magnetic fields
• Visualization of Branch Points in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>-Symmetric Waveguides
• Dimer with gain and loss: Integrability and ${\mathcal{P}}{\mathcal{T}}$-symmetry restoration
• Physical realization of -symmetric potential scattering in a planar slab waveguide
• Exponentially Fragile<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:math>Symmetry in Lattices with Localized Eigenmodes
• $\mathcal{PT}$-symmetric electronics
• An exactly solvable $\mathcal {PT}$-symmetric dimer from a Hamiltonian system of nonlinear oscillators with gain and loss

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