International Journal of Theoretical Physics

, Volume 54, Issue 11, pp 4027–4033 | Cite as

Spontaneous PT-Symmetry Breaking for Systems of Noncommutative Euclidean Lie Algebraic Type

  • Sanjib Dey
  • Andreas FringEmail author
  • Thilagarajah Mathanaranjan


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.


Euclidean algebras PT-symmetry Pseudo-Hermitian Hamiltonians Non-commutative quantum systems 



SD is supported by a City University Research Fellowship. TM is funded by an Erasmus Mundus scholarship and thanks City University for kind hospitality.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Sanjib Dey
    • 1
  • Andreas Fring
    • 1
    Email author
  • Thilagarajah Mathanaranjan
    • 1
  1. 1.Department of MathematicsCity University LondonLondonUK

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