论文标题
Fermi-Ulam模型的特征时间
Characteristic times for the Fermi-Ulam Model
论文作者
论文摘要
为Fermi-Ulam模型测量了平均庞加莱复发时间以及Lyapunov时间。我们确认平均复发时间取决于相位空间中选择的窗口的大小，以允许粒子复发。该区域的分形维度取决于复发时间的斜率在窗口的大小上，并测量了两个数值：（i）$μ$ = 1确认远离周期域和远离周期性域的混乱区域的正常扩散和； （ii）$μ$ = 2，导致在周期性区域附近测量的异常扩散，这是局部捕获颗粒的局部捕获的特征。 Lyapunov时间通过直接确定Lyapunov指数的直接确定在相空间中的不同域进行测量，实际上被定义为其反向。
The mean Poincarré recurrence time as well as the Lyapunov time are measured for the Fermi-Ulam model. We confirm the mean recurrence time is dependent on the size of the window chosen in the phase space to where particles are allowed to recur. The fractal dimension of the region is determined by the slope of the recurrence time against the size of the window and two numerical values were measured: (i) $μ$ = 1 confirming normal diffusion for chaotic regions far from periodic domains and; (ii) $μ$ = 2 leading to anomalous diffusion measured near periodic regions, a signature of local trapping of an ensemble of particles. The Lyapunov time is measured over different domains in the phase space through a direct determination of the Lyapunov exponent, indeed being defined as its inverse.
