Krein spaces and PT Quantum Mechanics
Krein spaces and PT Quantum Mechanics
Günther, U.
Abstract
A few basic facts about PT Quantum Mechanics (PTQM) are presented. Specifically, the underlying mathematical structures are briefly sketched, including Krein spaces (Hilbert spaces endowed with indefinite metric structures), J-selfadjointness, spectral singularities and PT phase transitions, the C-operator and the mapping between local PTQM and, in general, nonlocal conventional QM. The features are illustrated by following expamples: PT-symmetric Bose-Hubbard models (which may describe e.g. Bose-Einstein condensates with well balanced particle injection and extraction) and PT-symmetric brachistochrones and tachistochrones. Finally, recent realizations and applications in optical systems and microwave billiards are discussed --- including corresponding experiments.
Keywords: PT quantum mechanics; Krein spaces; spectral singularities; phase transitions; nonlocal quantum mechanics; Bose-Hubbard model; Bose-Einstein condensate; quantum brachistochrone; tachistochrone; optical systems; microwave billiards
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Eingeladener Vortrag (Konferenzbeitrag)
Physics Meeting in Amazonia, 24.-28.09.2012, Belem, Brazil
Permalink: https://www.hzdr.de/publications/Publ-17847