EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS

Authors

  • Hichem Eleuch Department of Physics, McGill University, Montreal
  • Ingrid Rotter Max Planck Institute for the Physics of Complex Systems, D-01187 Dresden

DOI:

https://doi.org/10.14311/AP.2014.54.0106

Abstract

Exceptional points (EPs) determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian) relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.

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Published

2014-04-30

How to Cite

Eleuch, H., & Rotter, I. (2014). EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS. Acta Polytechnica, 54(2), 106–112. https://doi.org/10.14311/AP.2014.54.0106

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Articles