Related papers: A new symmetry theory for non-Hermitian Hamiltonians

A new symmetry theory for non-Hermitian Hamiltonians

URL: http://arxiv.org/abs/2308.13619v3
Date: Sat, 6 Jan 2024 12:23:45 GMT
Title: A new symmetry theory for non-Hermitian Hamiltonians
Authors: Mustapha Maamache and Nour El Houda Absi
Abstract summary: The eta pseudo PT symmetry theory, denoted by the symbol eta, explores the conditions under which non-Hermitian Hamiltonians can possess real spectra.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The {\eta} pseudo PT symmetry theory, denoted by the symbol {\eta}, explores the conditions under which non-Hermitian Hamiltonians can possess real spectra despite the violation of PT symmetry, that is the adjoint of H, denoted H^{{\dag}} is expressed as H^{{\dag}}=PTHPT. This theory introduces a new symmetry operator, {\eta}=PT{\eta}, which acts on the Hilbert space. The {\eta} pseudo PT symmetry condition requires the Hamiltonian to commute with the {\eta} operator, leading to real eigenvalues. We discuss some general implications of our results for the coupled non hermitian harmonic oscillator.

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