开放Sinai台球中粒子输运性质的分形研究

Sinai量子台球能够模拟出混沌性质且数值运算相对简单, 成为研究微观体系动力学的理想模型。 本文以Sinai开放台球作为理论模型, 研究了粒子的逃逸, 并对逃逸中的碰撞次数进行了数值计算，得到的结果显示了初始条件对逃逸的重要性。采用简化的盒计数 (box-counting)算法分别计算了不同门电压和不同开口宽度对应的分形维数, 分析了Sinai台球中的门电压和开口宽度对体系混沌性质的影响。

Fractal analysis of particles transport properties in an open Sinai billiard

Sinai quantum billiard is an ideal model to investigate dynamic properties of a microscopic system because it can be used to simulate chaotic properties and the numerical computation is relatively simple. This paper addresses the escape of particles and numerically calculates the collision numbers in escape process with Sinai quantum billiards as a theoretical model Results indicate the significance of initial conditions for escape. We employ a simplified box-counting approach to calculate the fractal dimensions that are corresponding to different gate voltages and different aperture widths. We also analyze the influences.of gate voltage and aperture width in Sinai quantum billiards on chaotic behaviors.