2007/08/17 by Paulo E G Assis, Paulo E. G. Assis, Andreas Fring · 1 citation
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th #quant-ph
paper · pdf · doi:10.1088/1751-8113/41/24/244001
published as Journal of Physics A: Math. Theor. 41 (2008) 244001 · 21 pages
arxiv created 2007/08/17 · openalex publication_date 2008/06/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We investigate properties of the most general -symmetric non-Hermitian Hamiltonian of cubic order in the annihilation and creation operators as a ten-parameter family. For various choices of the parameters we systematically construct an exact expression for a metric operator and an isospectral Hermitian counterpart in the same similarity class by exploiting the isomorphism between operator and Moyal products. We elaborate on the subtleties of this approach. For special choices of the ten parameters the Hamiltonian reduces to various models previously studied, such as to the complex cubic potential, the so-called Swanson Hamiltonian or the transformed version of the from below unbounded quartic − x 4 -potential. In addition, it also reduces to various models not considered in the present context, namely the single-site lattice Reggeon model and a transformed version of the massive sextic ± x 6 -potential, which plays an important role as a toy model to identify theories with vanishing cosmological constant.