2021/06/30 by Gustavo M. Uhdre, Danilo Cius, Fabiano M. Andrade
Mathematics · Physics and Astronomy · #Classical mechanics #Context (archaeology) #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Hermitian matrix #Jaynes–Cummings model #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Nonlinear Waves and Solitons #Physics #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quantum optics #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1103/physreva.105.013703
published as Phys. Rev. A 105, 013703 (2022) · 9 pages, 2 figures, matches published version
openalex publication_date 2022/01/06 · arxiv created 2022/01/07 · arxiv updated 2022/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The theory of non-Hermitian systems and the theory of quantum deformations have attracted a great deal of attention in the past decades. In general, non-Hermitian Hamiltonians are constructed by an ad hoc manner. Here, we study the (2+1) Dirac oscillator and show that in the context of the \ensuremathκ-deformed Poincar'e-Hopf algebra its Hamiltonian is non-Hermitian but has real eigenvalues. The non-Hermiticity stems from the \ensuremathκ-deformed algebra. From the mapping in Bermudez et al., Phys. Rev. A 76, 041801(R) (2007), we propose the \ensuremathκ-Jaynes-Cummings and \ensuremathκ-anti-Jaynes-Cummings models, which describe an interaction between a two-level system with a quantized mode of an optical cavity in the \ensuremathκ-deformed context. We find that the \ensuremathκ deformation modifies the Zitterbewegung frequencies and the collapses and revivals of quantum oscillations. In particular, the total angular momentum in the z direction is not conserved anymore, as a direct consequence of the deformation.