RIKEN介观器件腔中粒子逃逸曲线的无标度区研究

RIKEN介观器件腔中的粒子逃逸曲线存在混沌性质，是研究分形及自相似结构的理想模型。本文通过对混沌逃逸曲线及无标度区的研究，发现自相似结构并用相似比进行了定义。通过不同自相似结构的对比，发现同一无标度区内相似比具有恒定性，并得到了相似比与分形维数的线性关系。该研究使相似比成为定量描述无标度区以及混沌性质的手段，为混沌性质的表征提供了新的方法。

Research on the scaleless band of particles escape curves in RIKEN mesoscopic device

Particle escape curves have the property of chaotics in a RIKEN mesoscopic device, so these curves are the ideal models to investigate fractals and self similar structures. We found self similar structures of the escape curves and defined them by similar ratio through the research on the chaotic escape curves and the scaleless band. We also discovered that the similar ratio is constant in the same scaleless band by the comparisons among different self similar structures. We further acquired the linear relationship between the similar ratios and fractal dimensions of the escape curves. Similar ratio is therefore a means to quantitatively describe the scaleless band and chaotic behaviors. This provides a new method to characterize the chaotic property of a mesoscopic system.