论文标题
谐波振荡器本本征的定位和定位
Localization and delocalization of eigenmodes of Harmonic Oscillators
论文作者
论文摘要
我们表征了与具有任意频率的耦合量子谐波振荡器系统的征量序列相对应的量子极限和半古典测量。一组半古典措施的结构很大程度上取决于每个解耦振荡器的频率之间的算术关系。特别是，我们表明，一旦这些频率不是固定基本频率的合理倍数，那么半古典措施的集合不是凸，因此，在经典的谐波振荡器下，无限的许多措施不是半经典的度量。
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures turns out to depend strongly on the arithmetic relations between frequencies of each decoupled oscillator. In particular, we show that as soon as these frequencies are not rational multiples of a fixed fundamental frequency, the set of semi-classical measures is not convex and therefore, infinitely many measures that are invariant under the classical harmonic oscillator are not semi-classical measures.
