Potzuweit A, Weich T, Barkhofen S, Kuhl U, Stöckmann H-J, Zworski M
Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, 35032 Marburg, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066205. doi: 10.1103/PhysRevE.86.066205. Epub 2012 Dec 5.
We present microwave experiments on the symmetry reduced five-disk billiard studying the transition from a closed to an open system. The measured microwave reflection signal is analyzed by means of the harmonic inversion and the counting function of the resulting resonances is studied. For the closed system this counting function shows the Weyl asymptotic with a leading exponent equal to 2. By opening the system successively this exponent decreases smoothly to a noninteger value. For the open systems the extraction of resonances by the harmonic inversion becomes more challenging and the arising difficulties are discussed. The results can be interpreted as a first experimental indication for the fractal Weyl conjecture for resonances.
我们展示了在对称性降低的五盘台球上进行的微波实验，该实验研究了从封闭系统到开放系统的转变。通过谐波反演分析测量到的微波反射信号，并研究所得共振的计数函数。对于封闭系统，该计数函数呈现出具有等于2的领先指数的魏尔渐近性。通过依次打开系统，该指数平滑地减小到一个非整数值。对于开放系统，通过谐波反演提取共振变得更具挑战性，并讨论了出现的困难。这些结果可被解释为共振的分形魏尔猜想的首个实验迹象。
