Berkolaiko G, Keating J P, Winn B
Department of Mathematics, University of Strathclyde, Glasgow G1 1XH, United Kingdom.
Phys Rev Lett. 2003 Sep 26;91(13):134103. doi: 10.1103/PhysRevLett.91.134103.
We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate the corresponding limit distribution. Second, we find that they can be strongly scarred, in the case of star graphs by short (unstable) periodic orbits and, in the case of Seba billiards, by certain families of orbits. We construct sequences of states which have such a limit. Our results are illustrated by numerical computations.
星型图和塞巴台球。首先，我们证明这些本征函数不是量子遍历的，并计算了相应的极限分布。其次，我们发现它们可能会出现强疤痕，对于星型图而言，是由短（不稳定）周期轨道导致的；对于塞巴台球而言，则是由某些轨道族导致的。我们构造了具有这种极限的态序列。我们的结果通过数值计算进行了说明。
