Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation

Abstract

We study the one-dimensional Dirac equation with local PT-symmetric potentials whose discrete eigenfunctions and continuum asymptotic eigenfunctions are eigenfunctions of the PT operator, too: on these conditions the bound-state spectra are real and the potentials are reflectionless and conserve unitarity in the scattering process. Absence of reflection makes it meaningful to consider also PT-symmetric potentials that do not vanish asymptotically.

24 pages, to appear in J. Phys. A : Math. Theor; one acknowledgement and one reference added

References in corpus (13)

• Making Sense of Non-Hermitian Hamiltonians
• Quantum simulation of the Dirac equation
• Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
• Exact Mapping of the 2+1 Dirac Oscillator onto the Jaynes-Cummings Model: Ion-Trap Experimental Proposal
• Interface between Hermitian and non-Hermitian Hamiltonians in a model calculation
• Scattering theory with localized non-Hermiticities
• The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry
• Discrete PT-symmetric models of scattering
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Overcritical PT-symmetric square well potential in the Dirac equation
• Scattering by PT-symmetric non-local potentials
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation
• On algebraic models of relativistic scattering

Cited by in corpus (8)

• Optical realization of relativistic non-Hermitian quantum mechanics
• Classical Simulation of Relativistic Quantum Mechanics in Periodic Optical Structures
• An exactly solvable quantum-lattice model with a tunable degree of nonlocality
• Pseudo Hermitian Generalized Dirac Oscillators
• Deconstructing non-dissipative non-Dirac-hermitian relativistic quantum systems
• Dirac equation with complex potentials
• Non-Hermitian CP-Symmetric Dirac Hamiltonians with Real Energy Eigenvalues
• Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics