München 2019 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 11: Teilchen und ihr Wechselwirkungen
MP 11.1: Talk
Thursday, March 21, 2019, 14:00–14:20, HS 23
Phase Spaces, Parity Operators, and the Born-Jordan Distribution — Bálint Koczor1, Frederik vom Ende1, Maurice de Gosson2, Steffen J. Glaser1, and •Robert Zeier3 — 1Technische Universität München, Department Chemie, Lichtenbergstrasse 4, 85747 Garching, Germany — 2Faculty of Mathematics (NuHAG), University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria — 3Adlzreiterstrasse 23, 80337 München, Germany
Phase spaces as given by the Wigner distribution function provide a natural description of infinite-dimensional quantum systems. They are an important tool in quantum optics and have been widely applied in the context of time-frequency analysis and pseudo-differential operators. Phase-space distribution functions are usually specified via integral transformations or convolutions which can be averted and subsumed by (displaced) parity operators proposed in this work. Building on earlier work by Grossmann for Wigner distribution functions, parity operators are used to define phase-space distribution functions as quantum-mechanical expectation values. These distribution functions are related to the so-called Cohen class and to various quantization schemes. Our approach is also applied to the Born-Jordan distribution which originates from the Born-Jordan quantization. The corresponding parity operator is written as a weighted average of both displacements and squeezing operators and we determine its generalized spectral decomposition. This leads to an efficient computation of the Born-Jordan parity operator and example quantum states reveal unique features of the Born-Jordan distribution. Refer to arxiv:1811.05872.