SUSY transformations between digonalizable and non-diagonalizable Hamiltonians
arXiv:quant-ph/0503075 · doi:10.1088/0305-4470/38/21/L04
Abstract
Recently (see quant-ph/0503040) an explicit example has been given of a PT-symmetric non-diagonalizable Hamiltonian. In this paper we show that such Hamiltonians appear as supersymmetric (SUSY) partners of Hermitian (hence diagonalizable) Hamiltonians and they can be turned back to diagonalizable forms by appropriate SUSY transformations.
References in corpus (5)
- Higher-Derivative Supersymmetry and the Witten Index
- Higher-order supersymmetric quantum mechanics
- New possibilities for supersymmetry breakdown in quantum mechanics and second order irreducible Darboux transformations
- New features in supersymmetry breakdown in quantum mechanics
- Is the CPT-norm always positive?
Cited by in corpus (30)
- Making Sense of Non-Hermitian Hamiltonians
- Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at real Energies
- Spectral singularities and Bragg scattering in complex crystals
- Projective Hilbert space structures at exceptional points
- Spectral Singularities, Biorthonormal Systems, and a Two-Parameter Family of Complex Point Interactions
- Resonance Phenomenon Related to Spectral Singularities, Complex Barrier Potential, and Resonating Waveguides
- Spectral singularities in PT-symmetric periodic finite-gap systems
- Optical lattices with exceptional points in the continuum
- Spectral singularities of non-Hermitian Hamiltonians and SUSY transformations
- Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
- Exceptional points and Bloch oscillations in non-Hermitian lattices with unidirectional hopping
- Talbot self-imaging in -symmetric complex crystals
- Scattering cross section resonance originating from a spectral singularity
- SUSY transformations with complex factorization constants. Application to spectral singularities
- Irreducible second order SUSY transformations between real and complex potentials
- Spectral Singularity in confined PT symmetric optical potential
- Pseudo-Hermiticity of an Exactly Solvable Two-Dimensional Model
- Supersymmetric Biorthogonal Quantum Systems
- Hermitian Hamiltonian equivalent to a given non-Hermitian one. Manifestation of spectral singularity
- Exact propagators for SUSY partners
- Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
- Non-Hermitian quantum rings
- Time evolution of decay for purely absorptive potentials: The effect of spectral singularities
- Exact propagators for complex SUSY partners of real potentials
- Equivalent Hermitian operator from supersymmetric quantum mechanics
- Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum
- Two-level systems: exact solutions and underlying pseudo-supersymmetry
- Exact Propagators for Soliton Potentials
- Spectral singularity in composite systems and simulation of a resonant lasing cavity
- Invisibility and PT Symmetry: A Simple Geometrical Viewpoint