On the {\eta} pseudo PT symmetry theory for non-Hermitian Hamiltonians: time-dependent systems

• URL: http://arxiv.org/abs/2308.13834v4
• Date: Wed, 27 Dec 2023 11:24:33 GMT
• Title: On the {\eta} pseudo PT symmetry theory for non-Hermitian Hamiltonians: time-dependent systems
• Authors: Mustapha Maamache
• Abstract summary: A non-Hermitian Hamiltonian H is related to its adjoint Hdag via the relation, Hdag=PTHPT. We propose a derivation of pseudo PT symmetry and eta -pseudo-Hermiticity simultaneously for the time dependent non-Hermitian Hamiltonians.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the context of non-Hermitian quantum mechanics, many systems are known to possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related to its adjoint H^{{\dag}} via the relation, H^{{\dag}}=PTHPT . We propose a derivation of pseudo PT symmetry and {\eta} -pseudo-Hermiticity simultaneously for the time dependent non-Hermitian Hamiltonians by intoducing a new metric {\eta}(t)=PT{\eta}(t) that not satisfy the time-dependent quasi-Hermiticity relation but obeys the Heisenberg evolution equation. Here, we solve the SU(1,1) time-dependent non-Hermitian Hamiltonian and we construct a time-dependent solutions by employing this new metric and discuss a concrete physical applications of our results.

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