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首页> 外文期刊>Physica Scripta: An International Journal for Experimental and Theoretical Physics >Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity
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Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

机译：量子和半经典自旋网络：从原子和分子物理学到量子计算和重力

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摘要

The mathematical apparatus of quantum-mechanical angular momentum (re) coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory-and of its extension to other Lie and quantum groups-by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments-such as for instance the hyperquantization algorithm-as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.
机译：最初用于描述原子，分子，光学和核物理中的光谱现象的量子力学角动量（re）耦合数学装置已嵌入现代代数环境中，该环境强调了基础的组合方面。 SU（2）耦合理论涉及Wigner的3nj符号，以及它们的计算，一般性质，大条目的渐近极限的相关问题，如今在量子引力和量子计算应用中也发挥着重要作用。我们使用“自旋网络”的总称来指代这一理论的组成部分，以及它对其他李和量子群的扩展。记录了与离散正交多项式数学理论（所谓的Askey方案）的已建立联系的最新进展，这些联系提供了基于渐进展开的强大工具，这些渐进展开在物理方面对应于半古典极限的各个级别。这些结果不仅在理论分子物理学中有用，而且对于激发分子动力学和化学反应理论（通常涉及大角动量）的计算要求很高的问题的激励算法也很有用。对于量子化学，这些技术的应用包括在原子和分子问题中，在构型空间（Sturmian轨道）或动量空间中对完整的正交基集进行选择和分类。在本文中，我们列出并讨论了这些发展的某些方面，例如超量化算法，以及在量子引力和拓扑学上的一些应用，从而为统一的背景结构提供了证据。

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