QT-Symmetry and Weak Pseudo-Hermiticity

Abstract

For an invertible (bounded) linear operator Q acting in a Hilbert space $\mathcal{H}$, we consider the consequences of the QT-symmetry of a non-Hermitian Hamiltonian $H:\mathcal{H}\to \mathcal{H}$ where T is the time-reversal operator. If H is symmetric in the sense that $\mathcal{T}{H}^{†}\mathcal{T}=H$, then QT-symmetry is equivalent to Q^{-1}-weak-pseudo-Hermiticity. But in general this equivalence does not hold. We show this using some specific examples. Among these is a large class of non-PT-symmetric Hamiltonians that share the spectral properties of PT-symmetric Hamiltonians.

Extended published version, includes a new section giving a new exactly solvable class of bosonic non-PT-symmetric and non-Hermitian Hamiltonians with a real spectrum, 10 pages

References in corpus (2)

• Is Weak Pseudo-Hermiticity Weaker than Pseudo-Hermiticity?
• Strengthened PT-symmetry with P $\ne$ P${}^{†}$

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• Alternative descriptions and bipartite compound quantum systems
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