The Experts below are selected from a list of 1974 Experts worldwide ranked by ideXlab platform
Vincenzo Aquilanti - One of the best experts on this subject based on the ideXlab platform.
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the screen representation of vector coupling Coefficients or wigner 3j symbols exact computation and illustration of the asymptotic behavior
arXiv: Quantum Physics, 2014Co-Authors: Ana Carla P Bitencourt, Mirco Ragni, Robert G Littlejohn, Roger W Anderson, Vincenzo AquilantiAbstract:The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan Coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the Coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.
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the discrete representation correspondence between quantum and classical spatial distributions of angular momentum vectors
Journal of Chemical Physics, 2006Co-Authors: Roger W Anderson, Vincenzo AquilantiAbstract:This work demonstrates that the quantum mechanical moments of a state described by the density matrix correspond to discrete spherical harmonic moments of the classical multipole expansion of the spatial distribution of the angular momentum vectors. For the diagonal density matrix elements, this work exploits the fact that the quantum mechanical vector coupling (Clebsch-Gordan) Coefficients become increasingly accurate discrete representations of spherical harmonics as j increases. A Schwinger-type basis accounts for nonaxially symmetric angular distributions, which result in nonzero off-diagonal elements of the density matrix. The resulting discrete minimum uncertainty picture of the classical moments has a stringent equivalence with the quantum mechanical one for all j and provides an unambiguous connection for the classical and quantum moments in the large j limit. The equivalence is numerically tested for simple models, and there is a satisfying equivalence even for small j. Applications, implications...
Ron Folman - One of the best experts on this subject based on the ideXlab platform.
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magic frequencies in atom light interaction for precision probing of the density matrix
Physical Review Letters, 2013Co-Authors: Moshe Givon, Allen Waxman, David Groswasser, Yonathan Japha, Yair Margalit, Tal David, Ron FolmanAbstract:We analyze theoretically and experimentally the existence of a {\it magic frequency} for which the absorption of a linearly polarized light beam by vapor alkali atoms is independent of the population distribution among the Zeeman sub-levels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancelation of the contributions of higher moments of the atomic density matrix, and is described using the Wigner-Eckart theorem and inherent properties of Clebsch-Gordan Coefficients. One important application is the robust measurement of the hyperfine population.
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magic frequencies in atom light interaction for precision probing of the density matrix
Physical Review Letters, 2013Co-Authors: Moshe Givon, Allen Waxman, David Groswasser, Yonathan Japha, Yair Margalit, Tal David, Ron FolmanAbstract:We analyze theoretically and experimentally the existence of a magic frequency for which the absorption of a linearly polarized light beam by a vapor of alkali-metal atoms is independent of the population distribution among the Zeeman sublevels and the angle between the beam and a magnetic field. The phenomenon originates from a peculiar cancellation of the contributions of higher moments of the atomic density matrix, and is described using the Wigner-Eckart theorem and inherent properties of Clebsch-Gordan Coefficients. One important application is the robust measurement of the hyperfine population.
Roger W Anderson - One of the best experts on this subject based on the ideXlab platform.
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the screen representation of vector coupling Coefficients or wigner 3j symbols exact computation and illustration of the asymptotic behavior
arXiv: Quantum Physics, 2014Co-Authors: Ana Carla P Bitencourt, Mirco Ragni, Robert G Littlejohn, Roger W Anderson, Vincenzo AquilantiAbstract:The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan Coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in discretization approximations. We point out the important role of the Regge symmetries for defining the screen where images of the Coefficients are projected, and for discussing their asymptotic properties and semiclassical behavior. Recursion relationships are formulated as eigenvalue equations, and exploited both for computational purposes and for physical interpretations.
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the discrete representation correspondence between quantum and classical spatial distributions of angular momentum vectors
Journal of Chemical Physics, 2006Co-Authors: Roger W Anderson, Vincenzo AquilantiAbstract:This work demonstrates that the quantum mechanical moments of a state described by the density matrix correspond to discrete spherical harmonic moments of the classical multipole expansion of the spatial distribution of the angular momentum vectors. For the diagonal density matrix elements, this work exploits the fact that the quantum mechanical vector coupling (Clebsch-Gordan) Coefficients become increasingly accurate discrete representations of spherical harmonics as j increases. A Schwinger-type basis accounts for nonaxially symmetric angular distributions, which result in nonzero off-diagonal elements of the density matrix. The resulting discrete minimum uncertainty picture of the classical moments has a stringent equivalence with the quantum mechanical one for all j and provides an unambiguous connection for the classical and quantum moments in the large j limit. The equivalence is numerically tested for simple models, and there is a satisfying equivalence even for small j. Applications, implications...
J. Van Der Jeugt - One of the best experts on this subject based on the ideXlab platform.
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Gel’fand-Zetlin Basis and Clebsch-Gordan Coefficients for Covariant Representations of the Lie superalgebra gl(m|n)
2015Co-Authors: Ni Stoilova, J. Van Der JeugtAbstract:A Gel’fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(m|n). Explicit expressions for the generators of the Lie superalgebra acting on this basis are determined. Furthermore, Clebsch-Gordan Coefficients corresponding to the tensor product of any covariant tensor representation of gl(m|n) with the natural represen-tation V ([1, 0,..., 0]) of gl(m|n) with highest weight (1,0,...,0) are computed. Both results are steps for the explicit construction of the parastatistics Fock space.
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Representations and Clebsch-Gordan Coefficients for the Jordanian quantum algebra Uh(sl(2)), preprint q-alg/9703011
2013Co-Authors: J. Van Der JeugtAbstract:Representation theory for the Jordanian quantum algebra Uh(sl(2)) is developed. Closed form expressions are given for the action of the generators of Uh(sl(2)) on the basis vectors of finite dimensional irreducible representations. It is shown how representation theory of Uh(sl(2)) has a close connection to combinatorial identities involving summation formulas. A general formula is obtained for the Clebsch-Gordan Coefficients Cj1,j2,j n1,n2,m(h) of Uh(sl(2)). These Clebsch-Gordan Coefficients are shown to coincide with those of su(2) for n1 + n2 ≤ m, but for n1 + n2> m they are in general a nonzero monomial in hn1+n2−m.
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Convolutions for orthogonal polynomials from Lie and quantum algebra representations
1998Co-Authors: H. T. Koelink, J. Van Der JeugtAbstract:Abstract. The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap Coefficients in the positive discrete series representations of the Lie algebra su(1, 1) and the Clebsch-Gordan decomposition leads to generalisations of the convolution identities for these polynomials. Using the Racah Coefficients convolution identities for continuous Hahn, Hahn and Jacobi polynomials are obtained. From the quantised universal enveloping algebra for su(1, 1) convolution identities for the Al-Salam and Chihara polynomials and the Askey-Wilson polynomials are derived by using the Clebsch-Gordan and Racah Coefficients. For the quantised universal enveloping algebra for su(2) q-Racah polynomials are interpreted as Clebsch-Gordan Coefficients, and the linearisation Coefficients for a two-parameter family of Askey-Wilson polynomials are derived. 1
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Convolutions For Orthogonal Polynomials From Lie And Quantum Algebra Representations
1996Co-Authors: H. T. Koelink, J. Van Der JeugtAbstract:. The interpretation of the Meixner-Pollaczek, Meixner and Laguerre polynomials as overlap Coefficients in the positive discrete series representations of the Lie algebra su(1; 1) and the Clebsch-Gordan decomposition leads to generalisations of the convolution identities for these polynomials. Using the Racah Coefficients convolution identities for continuous Hahn, Hahn and Jacobi polynomials are obtained. From the quantised universal enveloping algebra for su(1; 1) convolution identities for the Al-Salam and Chihara polynomials and the Askey-Wilson polynomials are derived by using the Clebsch-Gordan and Racah Coefficients. For the quantised universal enveloping algebra for su(2) q-Racah polynomials are interpreted as Clebsch-Gordan Coefficients, and the linearisation Coefficients for a two-parameter family of Askey-Wilson polynomials are derived. 1. Introduction The representation theory of Lie algebras and quantum algebras, or quantised universal enveloping algebras [9], is intimate..
Richard F Lebed - One of the best experts on this subject based on the ideXlab platform.
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su 3 clebsch gordan Coefficients for baryon meson coupling at arbitrary n c
Physical Review D, 2004Co-Authors: Thomas D Cohen, Richard F LebedAbstract:We present explicit formulas for the SU(3) Clebsch-Gordan Coefficients that are relevant for the couplings of large N{sub c} baryons to mesons. In particular, we compute the Clebsch-Gordan series for the coupling of the octet (associated with mesons, and remains the correct representation at large N{sub c}) to the large N{sub c} analogs of the baryon octet and decuplet representations.