Non-Hermitian Hamiltonians of Lie algebraic type
arXiv:0804.4677 · doi:10.1088/1751-8113/42/1/015203
Abstract
We analyse a class of non-Hermitian Hamiltonians, which can be expressed bilinearly in terms of generators of a sl(2,R)-Lie algebra or their isomorphic su(1,1)-counterparts. The Hamlitonians are prototypes for solvable models of Lie algebraic type. Demanding a real spectrum and the existence of a well defined metric, we systematically investigate the constraints these requirements impose on the coupling constants of the model and the parameters in the metric operator. We compute isospectral Hermitian counterparts for some of the original non-Hermitian Hamiltonian. Alternatively we employ a generalized Bogoliubov transformation, which allows to compute explicitly real energy eigenvalue spectra for these type of Hamiltonians, together with their eigenstates. We compare the two approaches.
27 pages
References in corpus (7)
- Making Sense of Non-Hermitian Hamiltonians
- conversion in nuclei within the CMSSM seesaw: universality versus non-universality
- PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
- Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian
- Exact Isospectral Pairs of PT-Symmetric Hamiltonians
- A complex periodic QES potential and exceptional points
- The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry