Pseudo-Hermitian systems with PT-symmetry: Degeneracy and Krein space

Autor:	Choutri, B., Cherbal, O., Ighezou, F. Z., Drir, M.
Rok vydání:	2016
Předmět:	Quantum Physics Mathematical Physics
Druh dokumentu:	Working Paper
DOI:	10.1007/s10773-017-3299-5
Popis:	We show in the present paper that pseudo-Hermitian Hamiltonian systems with even PT-symmetry admit a degeneracy structure. This kind of degeneracy is expected traditionally in the odd PT-symmetric systems which is appropriate to the fermions as shown by Jones-Smith and Mathur [1] who extended PT-symmetric quantum mechanics to the case of odd time-reversal symmetry. We establish that the pseudo-Hermitian Hamiltonians with even PT-symmetry admit a degeneracy structure if the operator PT anticommutes with the metric operator {\eta} which is necessarily indefinite. We also show that the Krein space formulation of the Hilbert space is the convenient framework for the implementation of unbroken PT-symmetry. These general results are illustrated with great details for four-level pseudo-Hermitian Hamiltonian with even PT-symmetry. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1610.08101 Zobrazit plný text záznamu View this record from Arxiv