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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 468, Pages 177–201
(Mi znsl6580)
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This article is cited in 6 scientific papers (total in 6 papers)
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On moduli space of the Wigner quasiprobability distributions for $N$-dimensional quantum systems
V. Abgaryana, A. Khvedelidzebca, A. Torosyana a Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980 Dubna, Russia
b A. Razmadze Mathematical Institute, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia
c Institute of Quantum Physics and Engineering Technologies, Georgian Technical University, Tbilisi, Georgia
Abstract:
A mapping between operators on the Hilbert space of $N$-dimensional quantum system and the Wigner quasiprobability distributions defined on the symplectic flag manifold is discussed. The Wigner quasiprobability distribution is constructed as a dual pairing between the density matrix and the Stratonovich–Weyl kernel. It is shown that the moduli space of the Stratonovich–Weyl kernel is given by an intersection of the coadjoint orbit space of the $SU(N)$ group and a unit $(N-2)$-dimensional sphere. The general consideration is exemplified by a detailed description of the moduli space of $2,3$ and $4$-dimensional systems.
Key words and phrases:
Wigner function, quasiprobability distribution, moduli space, group actions, Lie group orbits, Stratonovich–Weyl kernel.
Received: 11.09.2018
Citation:
V. Abgaryan, A. Khvedelidze, A. Torosyan, “On moduli space of the Wigner quasiprobability distributions for $N$-dimensional quantum systems”, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Zap. Nauchn. Sem. POMI, 468, POMI, St. Petersburg, 2018, 177–201; J. Math. Sci. (N. Y.), 240:5 (2019), 617–633
Linking options:
https://www.mathnet.ru/eng/znsl6580 https://www.mathnet.ru/eng/znsl/v468/p177
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Abstract page: | 120 | Full-text PDF : | 37 | References: | 20 |
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