QT-Symmetry and Weak Pseudo-Hermiticity

Details QT-Symmetry and Weak Pseudo-Hermiticity QT-Symmetry and Weak Pseudo-Hermiticity

2007-10-25

arxiv.org/abs/0710.4879v2

J. Phys. A: Math. Theo., 41 (2008) 055304 (8 pages)

Physics

Quantum Physics

Extended published version, includes a new section giving a new exactly solvable class of bosonic non-PT-symmetric and non-Her

Scientific paper

For an invertible (bounded) linear operator Q acting in a Hilbert space ${\cal H}$, we consider the consequences of the QT-symmetry of a non-Hermitian Hamiltonian $H:{\cal H}\to{\cal H}$ where T is the time-reversal operator. If H is symmetric in the sense that ${\cal T} H^\dagger {\cal T}=H$, 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.

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