自旋系统临界能区的半经典分析
Semi-classical Analysis of Spin Systems near Critical Energies
摘要：
研究了$su(2)$哈密顿量在临界经典能量$ε_c$附近的谱性质，在此能量下，相应的经典动力学呈现双曲点（HP）.当半经典参数$n^{-1}=(2s)^{-1}$趋于零时（其中$s$是系统的总自旋），在热力学极限下，得到了在$ε_c$附近本征值的代数关系的一般方法.给出了该方法的两个应用，并与数值方法进行了比较。矩阵元素的观测值，计算与$ε_c$附近的能量状态之间，也计算和示出与数值结果一致。
英文摘要：
The spectral properties of $su(2)$ Hamiltonians are studied for energies near the critical classical energy $ε_c$ for which the corresponding classical dynamics presents hyperbolic points (HP). A general method leading to an algebraic relation for eigenvalues in the vicinity of $ε_c$ is obtained in the thermodynamic limit, when the semi-classical parameter $n^{-1}=(2s)^{-1}$ goes to zero (where $s$ is the total spin of the system). Two applications of this method are given and compared with numerics. Matrix elements of observables, computed between states with energy near $ε_c$, are also computed and shown to be in agreement with the numerical results.
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