PT-symmetric deformations of integrable models

Abstract

We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and non-linear integrable field equations of Korteweg-de-Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models we provide three alternative deformations: A complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real valued field equations of non linear integrable systems and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of KdV-type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.

21 pages, 3 figures

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Cited by in corpus (26)

• Entanglement Entropy of Non Unitary Conformal Field Theory
• Integrable nonlocal Hirota equations
• On Symmetries and Exact Solutions of a Class of Non-local Non-linear Schrodinger Equations with Self-induced PT-symmetric Potential
• Entanglement Entropy of Non-Unitary Integrable Quantum Field Theory
• On integrable wave interactions and Lax pairs on symmetric spaces
• On the N-wave Equations with PT-symmetry
• Bohmian quantum trajectories from coherent states
• Nonlinear supersymmetry in the quantum Calogero model
• Asymptotic and scattering behaviour for degenerate multi-solitons in the Hirota equation
• Universal description of dissipative Tomonaga-Luttinger liquids with SU($N$) spin symmetry: Exact spectrum and critical exponents
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Perfectly invisible $\mathcal{P}\mathcal{T}$-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry
• Various Scattering Properties of a New PT-symmetric non-Hermitian potential
• Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain
• Nonlocal reductions of the Ablowitz-Ladik equation
• Conformal generation of an exotic rotationally invariant harmonic oscillator
• On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
• Complex BPS solitons with real energies from duality
• Hamiltonian formulation of systems with balanced loss-gain and exactly solvable models
• $\mathcal{P}\mathcal{T}$ deformation of angular Calogero models
• $\mathcal{P}\mathcal{T}$ deformation of Calogero-Sutherland models
• Nonlinear supersymmetry as a hidden symmetry
• Non-Hermitian superintegrable systems
• Calogero-like model without rearrangement symmetry
• Parity-Time Symmetric Spin-1/2 Richardson-Gaudin Models
• Free Particle to Complex KdV breathers through Isospectral Deformation