$\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry

Abstract

By applying the higher order Darboux algorithm to an exactly solvable non Hermitian $\mathcal{P}\mathcal{T}$ symmetric potential, we obtain a hierarchy of new exactly solvable non Hermitian $\mathcal{P}\mathcal{T}$ symmetric potentials with real spectra. It is shown that the symmetry underlying the potentials so generated and the original one is {\it nonlinear pseudo supersymmetry}. We also show that this formalism can be used to generate a larger class of new solvable potentials when applied to non Hermitian systems.

arXiv comment18 pages

References in corpus (36)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Supersymmetry and Quantum Mechanics
• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Localization transitions in non-Hermitian quantum mechanics
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Non-Hermitian Delocalization and Eigenfunctions
• PT -symmetric harmonic oscillators
• Higher-Derivative Supersymmetry and the Witten Index
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Quasi-exactly solvable quartic potential
• SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Second Order Derivative Supersymmetry and Scattering Problem
• Polynomial SUSY in Quantum Mechanics and Second Derivative Darboux Transformation
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
• N-fold Supersymmetry in Quantum Mechanics - General Formalism -
• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
• Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
• General Forms of a N-fold Supersymmetric Family
• Nonlinear Supersymmetry, Quantum Anomaly and Quasi-Exactly Solvable Systems
• SUSUSY quantum mechanics
• New features in supersymmetry breakdown in quantum mechanics
• PT-symetrically regularized Eckart,Poeschl-Teller and Hulthen potentials
• Second order SUSY transformations with `complex energies'
• Non-Hermitian supersymmetry and singular PT symmetrized oscillators
• Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
• Nonlinear supersymmetry on the plane in magnetic field and quasi-exactly solvable systems
• Bound States of Non-Hermitian Quantum Field Theories
• N-fold Supersymmetry for a Periodic Potential
• Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole
• New Exactly Solvable Isospectral Partners for PT Symmetric Potentials

Cited by in corpus (5)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry