标题： 量子四面体的大体积极限是一个量子谐振子 显示英文标题

标题： The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator

摘要： 结果显示，在大本征值区域，量子四面体的体积算符可以准确地由量子谐振子来描述。 这一结果基于以下事实：(i) 体积算符仅耦合其标准基中的相邻状态，(ii) 其矩阵元作为内部角动量量子数的函数表现出唯一的最大值。 这些量子数被视为连续变量，是描述其二次势能的振子的坐标，而相应的导数则定义了一个动量算符。 我们还分析了振子参数随四面体大小变化的标度性质，以及不同角动量耦合方案的作用。 显示英文摘要

摘要： It is shown that the volume operator of a quantum tetrahedron is, in the sector of large eigenvalues, accurately described by a quantum harmonic oscillator. This result relies on the fact that (i) the volume operator couples only neighboring states of its standard basis, and (ii) its matrix elements show a unique maximum as a function of internal angular momentum quantum numbers. These quantum numbers, considered as a continuous variable, are the coordinate of the oscillator describing its quadratic potential, while the corresponding derivative defines a momentum operator. We also analyze the scaling properties of the oscillator parameters as a function of the size of the tetrahedron, and the role of different angular momentum coupling schemes.