2014/07/30 by Sanjib Dey, Andreas Fring, Thilagarajah Mathanaranjan
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic number #Euclidean geometry #Geometry #Lie algebra #Lie group #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative geometry #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum mechanics #Spontaneous symmetry breaking #Symmetry (geometry) #Symmetry breaking #Type (biology) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1007/s10773-014-2447-4
published as International Journal of Theoretical Physics 54 (2015) 4027-4033 · 7 pages
arxiv created 2014/07/30 · openalex publication_date 2014/12/19 · arxiv updated 2015/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose a noncommutative version of the Euclidean Lie algebra E2. Several types of non-Hermitian Hamiltonian systems expressed in terms of generic combinations of the generators of this algebra are investigated. Using the breakdown of the explicitly constructed Dyson maps as a criterium, we identify the domains in the parameter space in which the Hamiltonians have real energy spectra and determine the exceptional points signifying the crossover into the different types of spontaneously broken PT-symmetric regions with pairs of complex conjugate eigenvalues. We find exceptional points which remain invariant under the deformation as well as exceptional points becoming dependent on the deformation parameter of the algebra.