Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity - Quantum PhysicsReport as inadecuate




Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity - Quantum Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: The mathematical apparatus of quantum-mechanical angular momentumrecoupling, developed originally to describe spectroscopic phenomena inatomic, molecular, optical and nuclear physics, is embedded in modern algebraicsettings which emphasize the underlying combinational aspects. SU2 recouplingtheory, involving Wigner-s 3nj symbols, as well as the related problems oftheir calculations, general properties, asymptotic limits for large entries,play nowadays a prominent role also in quantum gravity and quantum computingapplications. We refer to the ingredients of this theory -and of its extensionto other Lie and quantum group- by using the collective term of `spinnetworks-. Recent progress is recorded about the already establishedconnections with the mathematical theory of discrete orthogonal polynomialsthe so-called Askey Scheme, providing powerful tools based on asymptoticexpansions, which correspond on the physical side to various levels ofsemi-classical limits. These results are useful not only in theoreticalmolecular physics but also in motivating algorithms for the computationallydemanding problems of molecular dynamics and chemical reaction theory, wherelarge angular momenta are typically involved. As for quantum chemistry,applications of these techniques include selection and classification ofcomplete orthogonal basis sets in atomic and molecular problems, either inconfiguration space Sturmian orbitals or in momentum space. In this paper welist and discuss some aspects of these developments -such as for instance thehyperquantization algorithm- as well as a few applications to quantum gravityand topology, thus providing evidence of a unifying background structure.



Author: V. Aquilanti, A.C.P. Bitencourt, C. da S. Ferreira, A. Marzuoli, M. Ragni

Source: https://arxiv.org/







Related documents