Spontaneous PT-symmetry breaking for systems of noncommutative Euclidean Lie algebraic type

Abstract

We propose a noncommutative version of the Euclidean Lie algebra $E_2$. 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.

7 pages

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• A new non-Hermitian E2-quasi-exactly solvable model
• An introductory review on resource theories of generalized nonclassical light
• Two dimensional non-Hermitian harmonic oscillator: coherent states
• A unifying E2-quasi-exactly solvable model