Sawada Shin-ichi, Taniguchi Tooru
Department of Physics, Kwansei Gakuin University, Sanda 669-1337, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Aug;88(2):022907. doi: 10.1103/PhysRevE.88.022907. Epub 2013 Aug 7.
We investigate dynamical properties of the system of two interacting hard disks within a circular billiard numerically in the case of zero total angular momentum. Varying the radius of two identical disks, we examine chaotic irregularity and ergodicity of the system. Single-particle configuration and velocity distributions are obtained from dynamical trajectory calculations and compared with those in the microcanonical ensemble. We also analyze properties of trajectories by calculating the finite-time maximum Lyapunov exponent and clarify the existence of sticky motions around Kolmogorov-Arnold-Moser (KAM) tori even for small radii of disks. It is shown that the present system is almost ergodic in spite of the existence of tori for small radii of disks since the ratio of tori to the whole phase space is extremely small. On the other hand, a number of tori increase abruptly as the radius of disks increases beyond some value and tori prevent trajectories to run over the phase space uniformly, which makes the ergodicity of the system broken down.
我们在总角动量为零的情况下，对圆形台球桌内两个相互作用的硬磁盘系统的动力学性质进行了数值研究。通过改变两个相同磁盘的半径，我们研究了系统的混沌不规则性和遍历性。从动力学轨迹计算中获得单粒子构型和速度分布，并与微正则系综中的分布进行比较。我们还通过计算有限时间最大李雅普诺夫指数来分析轨迹的性质，并阐明即使对于小半径磁盘，在柯尔莫哥洛夫 - 阿诺尔德 - 莫泽（KAM）环面周围也存在粘性运动。结果表明，尽管对于小半径磁盘存在环面，但由于环面在整个相空间中所占比例极小，当前系统几乎是遍历的。另一方面，当磁盘半径增加到超过某个值时，环面数量会突然增加，环面会阻止轨迹均匀地遍历相空间，从而导致系统的遍历性被破坏。
