Publications Repository - Helmholtz-Zentrum Dresden-Rossendorf

1 Publication

Krein space related physics: from mathematical structures towards experiments

Günther, U.


A compact overview is given about physical systems with antilinear symmetries as they have been intensively studied during the past 15 years and as they are currently still under intensive investigation worldwide. Starting from a few comments on the historical background, the underlying basic mathematical structures are sketched. This especially concerns the properties of the corresponding effective Hamiltonians, their non-selfadjointness in usual Hilbert spaces with positive definite (Euclidean type) inner products and their selfadjointness in Hilbert spaces with indefinite inner products, so called Krein spaces. Specific properties of these Hamiltonians like non-diagonalizability at spectral branch-points, hidden Jordan block structures, perturbation theory in terms of Puisseux series expansions instead of Taylor expansions as well as related group structures will be briefly discussed. Realizations of the antilinear symmetries are demonstrated for physical systems with simultaneous time-reversal and parity-inversion symmetries (PT symmetries). Specific physical effects like PT phase transitions and exciting new features of these systems are illustrated on simulations for various optical waveguide systems, Bose-Einstein condensates (BECs), microwave cavities, systems of coupled oscillators etc. Finally, a brief overview is given about recent experimental implementations as well as about a couple of promising new directions of research with interconnections to other areas of active research in theoretical and experimental physics.

Keywords: PT physics; PT phase transitions; operator theory; Krein spaces; branch points; Jordan blocks; Puisseux series expansions; Bose-Einstein condensates; optical waveguide systems; microwave cavities

  • Lecture (others)
    Lecture presented at the Physics Department, College of Sciences, Koc University, Istanbul, 16.12.2013, Istanbul, Turkey