Stadium型介观器件腔中粒子逃逸率的研究

Escape rates of particles in Stadium mesoscopic devices

本文研究了粒子在二维弱开口的Bunimovich Stadium型介观混沌器件中的逃逸规律.利用经典统计的方法,通过改变器件端口宽度、圆弧半径及器件腔长等参数,首次发现随器件各项参数变化的分形维数与粒子逃逸率趋势符合,并揭示了混沌体系的逃逸指数受器件形状的影响.统计并拟合了粒子逃逸率与粒子波数大小的关系,数值结果表明,粒子逃逸率与波数为二次函数关系,但逃逸率与能量大小不是严格的线性关系.进一步分析了在器件入口处粒子的衍射效应对粒子逃逸的影响,结果表明,衍射效应使粒子逃逸率增加,且粒子数的演化在时间较短时不再满足指数关系,长时间的演化再次满足指数衰减规律.

We have studied the chaotic escape of particles in a two-dimensional weakly opened mesoscopic components of the Bunimovich Stadium devices. Within the framework of classical statistics, we get the change of the fractal dimensions and the escape rates in several parameters of the device, such as the opening width, the arc radius and the cavity length. We first find the good agreement between the fractal dimensions and the escape rates, and reveal that the exponential law of escape is affected by the shape of device. We count and fit the relationship between the escape rates and the wave numbers of the particles. As is shown in the numerical results, the relation between the escape rates and the wave numbers is a quadratic function, but the escape rates are not strictly linearly varied with the change of the energy. Furthermore, we analyze the influence of diffraction at the lead opening on the escape of the particles. Numerical results show that the diffraction effect makes the escape rates increase, and the evolution of the number of particles no longer obeys the law of exponential decay in a short time, but observes it again in a long time.