Correspondence Rules for SU(1,1) Quasidistribution Functions and Quantum Dynamics in the Hyperbolic Phase Space

Correspondence Rules for SU(1,1) Quasidistribution Functions and Quantum Dynamics in the Hyperbolic Phase Space

We derive the explicit differential form for the action of the generators of the SU(1,1) group on the corresponding s-parametrized symbols. This allows us to obtain evolution equations for the phase-space functions on the upper sheet of the two-sheet hyperboloid and analyze their semiclassical limit...

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Veröffentlicht in:Entropy (Basel, Switzerland) Switzerland), 2022-10, Vol.24 (11), p.1580
Hauptverfasser: Baltazar, Miguel, Valtierra, Iván F., Klimov, Andrei B.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Correspondence
Generators
Hamiltonian functions
Hilbert space
Partial differential equations
phase space
Quantum theory
SU(1,1) group
Symmetry
Wigner function
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Beschreibung
Zusammenfassung:We derive the explicit differential form for the action of the generators of the SU(1,1) group on the corresponding s-parametrized symbols. This allows us to obtain evolution equations for the phase-space functions on the upper sheet of the two-sheet hyperboloid and analyze their semiclassical limits. Dynamics of quantum systems with SU(1,1) symmetry governed by compact and non-compact Hamiltonians are discussed in both quantum and semiclassical regimes.
ISSN:1099-4300
1099-4300
DOI:10.3390/e24111580