Blum Galya, Gnutzmann Sven, Smilansky Uzy
The Weizmann Institute of Science, 76100 Rehovot, Israel.
Phys Rev Lett. 2002 Mar 18;88(11):114101. doi: 10.1103/PhysRevLett.88.114101. Epub 2002 Mar 1.
We consider the distribution of the (properly normalized) numbers of nodal domains of wave functions in 2D quantum billiards. We show that these distributions distinguish clearly between systems with integrable (separable) or chaotic underlying classical dynamics, and for each case the limiting distribution is universal (system independent). Thus, a new criterion for quantum chaos is provided by the statistics of the wave functions, which complements the well-established criterion based on spectral statistics.
我们考虑二维量子台球中波函数节点域（经过适当归一化）数量的分布。我们表明，这些分布能清晰地区分具有可积（可分离）或混沌基础经典动力学的系统，并且在每种情况下，极限分布都是通用的（与系统无关）。因此，波函数的统计为量子混沌提供了一个新的判据，它补充了基于谱统计的成熟判据。
