3nj Morphogenesis and Semiclassical Disentangling

Abstract

Recoupling coefficients (3nj symbols) are unitary transformations between binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum operators. They have been used in a variety of applications in spectroscopy, quantum chemistry and nuclear physics and quite recently also in quantum gravity and quantum computing. These coefficients, naturally associated to cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and analytical features that make them fashinating objects to be studied on their own. In this paper we develop a bottom--up, systematic procedure for the generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and algebraic methods. We provide also a novel approach to the problem of classifying various regimes of semiclassical expansions of 3nj coefficients (asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial, analytical and numerical tools.

References in corpus (4)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• Semiclassical analysis of Wigner $3j$-symbol
• Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity
• Surface embedding, topology and dualization for spin networks

Cited by in corpus (16)

• Asymptotics of the Wigner 9j symbol
• A new Hamiltonian for the Topological BF phase with spinor networks
• Generating Functions for Coherent Intertwiners
• Semiclassical Analysis of the Wigner $9J$-Symbol with Small and Large Angular Momenta
• The Screen representation of spin networks: 2D recurrence, eigenvalue equation for 6j symbols, geometric interpretation and Hamiltonian dynamics
• Asymptotics of Wigner 3nj-symbols with Small and Large Angular Momenta: an Elementary Method
• Geometry of the shears mechanism in nuclei
• The screen representation of vector coupling coefficients or Wigner 3j symbols: exact computation and illustration of the asymptotic behavior
• Quantum Tetrahedra
• Symplectic and Semiclassical Aspects of the Schläfli Identity
• Lessons from Toy-Models for the Dynamics of Loop Quantum Gravity
• Symmetric angular momentum coupling, the quantum volume operator and the 7-spin network: a computational perspective
• Quadrilaterals on the square screen of their diagonals: Regge symmetries of quantum-mechanical spin-networks and Grashof classical mechanisms of four-bar linkages
• A New Recursion Relation for the 6j-Symbol
• The Hilbert space costratification for the orbit type strata of SU(2)-lattice gauge theory
• Exact and asymptotic computations of elementary spin networks: classification of the quantum-classical boundaries