Escape rates of particles in Stadium mesoscopic devices

Abstract

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.