Symbol Correspondences for Spin Systems

Rios, Pedro Paulo de Magalhães; Straume, Eldar

doi:10.1007/978-3-319-08198-4

Cited by 13 publications

(11 citation statements)

References 69 publications

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“…was found in [45,46] (see also [47]) and has a somewhat involved form given in equation (B.1) of the appendix. In what follows we examine its approximate form in the asymptotic limit S 1 .…”

Section: The Kernel and Some Properties Of The Resulting Mappingsmentioning

confidence: 95%

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GeneralizedSU(2) covariant Wigner functions and some of their applications

Klimov¹,

Romero²,

Guise³

2017

J. Phys. A: Math. Theor.

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Section: The Kernel and Some Properties Of The Resulting Mappingsmentioning

confidence: 95%

“…[32,25,37]), but rarely useful in practical calculations. Instead, a differential form of the star-product operation, emphasizing the local nature of the phase space approach, is known for systems with Heisenberg-Weyl [16,38], E(2) [44] and SU (2) [45][46][47] and some generalizations [48,49].…”

Section: Topical Reviewmentioning

confidence: 99%

GeneralizedSU(2) covariant Wigner functions and some of their applications

Klimov¹,

Romero²,

Guise³

2017

J. Phys. A: Math. Theor.

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“…In this section, we clarify connections between the proposed generic SW mapping and a well elaborated SU(2)-symmetric spin-j symbol correspondence. To make the presentation self-sufficient, we start with the definitions of the spin-j system and a spin-j symbol correspondence in the form presented in the work by de Rios and Straum [21]. Definition 1.…”

Section: Reduction To Su(2) Symmetric Spin-j Correspondencementioning

confidence: 99%

On Families of Wigner Functions for N-Level Quantum Systems

Abgaryan

Khvedelidze

2021

Symmetry

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A method for constructing all admissible unitary non-equivalent Wigner quasiprobability distributions providing the Stratonovic-h-Weyl correspondence for an arbitrary N-level quantum system is proposed. The method is based on the reformulation of the Stratonovich–Weyl correspondence in the form of algebraic “master equations” for the spectrum of the Stratonovich–Weyl kernel. The later implements a map between the operators in the Hilbert space and the functions in the phase space identified by the complex flag manifold. The non-uniqueness of the solutions to the master equations leads to diversity among the Wigner quasiprobability distributions. It is shown that among all possible Stratonovich–Weyl kernels for a N=(2j+1)-level system, one can always identify the representative that realizes the so-called SU(2)-symmetric spin-j symbol correspondence. The method is exemplified by considering the Wigner functions of a single qubit and a single qutrit.

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“…, l, we have that the commutation rules of spherical harmonics are such that the bracket of (l, m) and (l , m ) is non-zero only for harmonics of the form (l , m+m ). l ≡ l+ l +1(2) [15]. This simple fact implies that the interaction of two Rossby waves may be restricted to some specific part of the phase space.…”

Section: Introductionmentioning

confidence: 99%

An algebraic approach to the spontaneous formation of spherical jets

Viviani¹

2021

Preprint

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The global structure of the atmosphere and the oceans is a continuous source of intriguing challenges in geophysical fluid dynamics (GFD). Among these, jets are determinant in the air and water circulation around the Earth. In the last fifty years, thanks to the development of more and more precise and extensive observations, it has been possible to study in detail the atmospheric formations of the giant-gas planets in the solar system. For those planets, jets are the dominant large scale structure. Since the 70s various theories combining observations and mathematical models have been proposed in order to describe their formation and stability. In this paper, we propose a purely algebraic approach to describe the spontaneous formation of jets on a spherical domain. Analysing the algebraic properties of the 2D Euler equations, we give a complete characterization of the jet formations. In view of the applications and the numeric integration of the Euler equations, we show how the jets formation also appear in the discrete Zeitlin model of the Euler equations. For this model, the classification of the jet formations can be precisely described in terms of reductive Lie algebra decomposition. Our results provide a simple mechanism for the jets formation, which can be directly applied in the numerical integration of their dynamics.

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Symbol Correspondences for Spin Systems

Cited by 13 publications

References 69 publications

GeneralizedSU(2) covariant Wigner functions and some of their applications

GeneralizedSU(2) covariant Wigner functions and some of their applications

On Families of Wigner Functions for N-Level Quantum Systems

An algebraic approach to the spontaneous formation of spherical jets

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