Projective Hilbert space structures at exceptional points

  title={Projective Hilbert space structures at exceptional points},
  author={Uwe G{\"u}nther and Ingrid Rotter and Boris F. Samsonov},
A non-Hermitian complex symmetric 2 × 2-matrix toy model is used to study projective Hilbert space structures in the vicinity of exceptional points (EPs). The bi-orthogonal eigenvectors of a diagonalizable matrix are Puiseuxexpanded in terms of the root vectors at the EP. It is shown that the apparent contradiction between the two incompatible normalization conditions with finite and singular behaviour in the EP-limit can be resolved by projectively extending the original Hilbert space. The… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 29 references

Analytic Perturbation Theory for Matrices and Operators (Berlin: Akademie-Verlag) Baumgärtel H

  • H Baumgärtel
  • 1984
Highly Influential
5 Excerpts

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime (in preparation

  • E NBulgakov, I Rotter, A FSadreev
  • Phys. Rev. E
  • 2006
Highly Influential
3 Excerpts

Geometry, Topology and Physics (Bristol: Institute of Physics Publishing

  • M Nakahara
  • 1990
Highly Influential
3 Excerpts

Is PT -symmetric quantum mechanics just quantum mechanics in a non-orthogonal basis

  • D Martin
  • 2007
1 Excerpt

Making sense of non-Hermitian Hamiltonians Preprint hep-th/0703096

  • C MBender
  • 2007
2 Excerpts

Earth Planet

  • G Gerbeth, M Xu
  • Sci . Lett .
  • 2006


  • U Günther, F Stefani
  • J . Phys .
  • 2005

Topics in Cohomological Studies of Algebraic Varieties

  • P Pragacz
  • Impanga Lecture Notes (Basel: Birkhäuser)
  • 2005
3 Excerpts