Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica Scripta

Differential form of the correspondence rules for the generalized SU(2) Wigner functions

B Preciado, José Luis Romero, A. B. Klimov

Published Feb 1, 2012• 1 citation
Publisher

Abstract

Explicit correspondence rules for the operators from su(2) and h(1) algebras are found in the framework of the generalized Wigner-like quasidistribution function applied to describe quantum systems with the SU(2) dynamic symmetry group. These correspondence rules are used to analyze the quantum dynamics in the semiclassical limit.
DOI
10.1088/0031-8949/2012/t147/014027

Related papers

A generalized Wigner function for quantum systems with theSU(2) dynamical symmetry group

A. B. Klimov, José Luis Romero

We introduce a Wigner-like quasidistribution function to describe quantum systems with the SU (2) dynamic symmetry group. This function is defined in a three-dimensional group manifold and can be used to represent the states defined in several SU (2) invariant subspaces. The explicit differential Moyal-like form of the star product is found and analyzed in the semiclassical limit.

Journal of Physics A Mathematical and Theoretical•Jan 23, 2008•39 citations

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

Miguel Baltazar, Ivan F. Valtierra, A. B. Klimov

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.

Entropy•Oct 31, 2022•3 citations

Semiclassical phase-space dynamics of compound quantum systems:SU(2) covariant approach

K Tomatani, José Luis Romero, A. B. Klimov

The semiclassical evolution of the generalized SU (2) Wigner function for quantum systems with a variable number of excitations is discussed in detail. It is shown that in the framework of the Liouvillian approach quantum dynamics can be approximately described in terms of classical trajectories on an appropriate four-dimensional symplectic manifold. The analysis of this manifold allows the introduction of a phase-like observable that can be interpreted as a relative phase ‘between’ invariant subspaces.

Journal of Physics A Mathematical and Theoretical•May 8, 2015•4 citations

Quasiclassical and Quantum Systems of Angular Momentum. Part I. Group Algebras as a Framework for Quantum-Mechanical Models with Symmetries

Jan Jerzy Sławianowski, Vasyl Kovalchuk, Agnieszka Martens +2 more

We use the mathematical structure of group algebras and $H^{+}$-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are ${\rm SU}(2)$ and its quotient ${\rm SO}(3,\mathbb{R})$. The scheme developed is applied in two different contexts. Firstly, the purely group-algebraic framework is applied to the system of angular momenta of arbitrary origin, e.g., orbital angular momenta of electrons and nucleons, systems of quantized angular momenta of rotating extended objects like molecules. The other promising area of applications is Schrödinger quantum mechanics of rigid body with its often rather unexpected and very interesting features. Even within this Schrödinger framework the algebras of operators related to group algebras are a very useful tool. We investigate some problems of composed systems and the quasiclassical limit obtained as the asymptotics of "large" quantum numbers, i.e., "quickly oscillating" functions on groups. They are related in an interesting way to geometry of the coadjoint orbits of ${\rm SU}(2)$.

arXiv:1007.4121•Jul 23, 2010•4 citations

Phase Space Insights: Wigner Functions for Qubits and Beyond

Luis Lorenzo Sánchez-Soto, Ariana S. Muñoz, Pablo de la Hoz +2 more

Phase space methods, particularly Wigner functions, provide intuitive tools for representing and analyzing quantum states. We focus on systems with SU(2) dynamical symmetry, which naturally describes spin and a wide range of two-mode quantum models. We present a unified phase space framework tailored to these systems, highlighting its broad applicability in quantum optics, metrology, and information. After reviewing the core SU(2) phase-space formalism, we apply it to states designed for optimal quantum sensing, where their nonclassical features are clearly revealed in the Wigner representation. We then extend the approach to systems with an indefinite number of excitations, introducing a generalized framework that captures correlations across multiple SU(2)-invariant subspaces. These results offer practical tools for understanding both theoretical and experimental developments in quantum science.

Applied Sciences•May 6, 2025•6 citations

Correspondence rules for Wigner functions over S U ( 3 ) / U ( 2 )

Alex Clésio Nunes Martins, Andrei B Klimov, Hubert de Guise

Abstract We present results on the product for Wigner functions over . In particular, we present a form of the so-called correspondence rules, which provide a differential form of the product and when is an generator. For the Wigner map, these rules must contain second order derivatives and thus substantially differ from the rules of other known cases.

arXiv:1905.07597•Journal of Physics A Mathematical and Theoretical•May 17, 2019•4 citations
The semiclassical evolution of the generalized SU (2) Wigner function for quantum systems with a variable number of excitations is discussed in detail. It is shown that in the framework of the Liouvillian approach quantum dynamics can be approximately described in terms of classical trajectories on an appropriate four-dimensional symplectic manifold. The analysis of this manifold allows the introduction of a phase-like observable that can be interpreted as a relative phase ‘between’ invariant subspaces.
We use the mathematical structure of group algebras and H+H^{+}H+-algebras for describing certain problems concerning the quantum dynamics of systems of angular momenta, including also the spin systems. The underlying groups are SU(2){\rm SU}(2)SU(2) and its quotient SO(3,R){\rm SO}(3,\mathbb{R})SO(3,R). The scheme developed is applied in two different contexts. Firstly, the purely group-algebraic framework is applied to the system of angular momenta of arbitrary origin, e.g., orbital angular momenta of electrons and nucleons, systems of quantized angular momenta of rotating extended objects like molecules. The other promising area of applications is Schrödinger quantum mechanics of rigid body with its often rather unexpected and very interesting features. Even within this Schrödinger framework the algebras of operators related to group algebras are a very useful tool. We investigate some problems of composed systems and the quasiclassical limit obtained as the asymptotics of "large" quantum numbers, i.e., "quickly oscillating" functions on groups. They are related in an interesting way to geometry of the coadjoint orbits of SU(2){\rm SU}(2)SU(2).
Phase space methods, particularly Wigner functions, provide intuitive tools for representing and analyzing quantum states. We focus on systems with SU(2) dynamical symmetry, which naturally describes spin and a wide range of two-mode quantum models. We present a unified phase space framework tailored to these systems, highlighting its broad applicability in quantum optics, metrology, and information. After reviewing the core SU(2) phase-space formalism, we apply it to states designed for optimal quantum sensing, where their nonclassical features are clearly revealed in the Wigner representation. We then extend the approach to systems with an indefinite number of excitations, introducing a generalized framework that captures correlations across multiple SU(2)-invariant subspaces. These results offer practical tools for understanding both theoretical and experimental developments in quantum science.