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Non-Hermitian CP-Symmetric Dirac Hamiltonians with Real Energy Eigenvalues

A. D. Alhaidari

We present a large class of non-Hermitian non-PT-symmetric two-component Dirac Hamiltoninas with real energy spectra. These Hamiltonians are invariant under the combined action of “charge” conjugation (two-component transpose) and space-parity. Examples are given from the two subclasses of these systems having localized and/or continuum states with real energies.

http://arxiv.org/abs/1301.2056

Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)

Pseudo Hermitian Generalized Dirac Oscillators

D. Dutta, O. Panella, P. Roy

We study generalized Dirac oscillators with complex interactions in $$(1+1)$$ dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are $$\eta$$ pseudo Hermitian with respect to certain metric operators $$\eta$$. Exact solutions of the generalized Dirac Oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with Anti Jaynes Cummings type model and by spin flip it can also be identified with Jaynes Cummings type model.

http://arxiv.org/abs/1301.2035
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)