标题： 软墙对动力系统中相互作用粒子的影响 显示英文标题

标题： Soft wall effects on interacting particles in billiards

摘要： 物理上可实现的壁势（软壁）对一维（1D）弹道中两个相互作用粒子动力学的影响进行了数值研究。 1D 壁通过误差函数进行建模，通过改变软度参数$\sigma$可以连续分析从硬壁到软壁的转变。 对于$\sigma\to 0$，得到 1D 硬壁极限，相应的壁力是$\delta$-函数。 在这个极限下，相互作用粒子的动力学与之前针对 1D 硬壁获得的结果一致。 我们表明，在 1D 软壁模型中的两个相互作用粒子等价于一个粒子在一个软直角三角形弹道中。 $\sigma$的非常小的值显著改变了弹道内部的动力学，由于低能双碰撞（同时粒子-粒子-1D 壁碰撞）出现的规则岛导致平均有限时间李雅普诺夫指数显著下降。 由 1D 壁软度引起的规则岛和粘滞轨迹的增加通过最可能的有限时间李雅普诺夫指数的出现次数进行量化。 另一方面，系统的混沌运动是由于高能双碰撞引起的。 一般来说，我们观察到当$\sigma$增加时，平均有限时间李雅普诺夫指数减少，但最可能的有限时间李雅普诺夫指数的出现次数增加，这意味着相空间动力学趋于更加遍历性。 我们的结果表明，由弹道建模的周期结构中相互作用粒子的输运效率和热传导将强烈受到物理上可实现壁的平滑度的影响。 显示英文摘要

摘要： The effect of physically realizable wall potentials (soft walls) on the dynamics of two interacting particles in a one-dimensional (1D) billiard is examined numerically. The 1D walls are modeled by the error function and the transition from hard to soft walls can be analyzed continuously by varying the softness parameter $\sigma$. For $\sigma\to 0$ the 1D hard wall limit is obtained and the corresponding wall force on the particles is the $\delta$-function. In this limit the interacting particle dynamics agrees with previous results obtained for the 1D hard walls. We show that the two interacting particles in the 1D soft walls model is equivalent to one particle inside a soft right triangular billiard. Very small values of $\sigma$ substantiously change the dynamics inside the billiard and the mean finite-time Lyapunov exponent decreases significantly as the consequence of regular islands which appear due to the low-energy double collisions (simultaneous particle-particle-1D wall collisions). The rise of regular islands and sticky trajectories induced by the 1D wall softness is quantified by the number of occurrences of the most probable finite-time Lyapunov exponent. On the other hand, chaotic motion in the system appears due to the high-energy double collisions. In general we observe that the mean finite-time Lyapunov exponent decreases when $\sigma$ increases, but the number of occurrences of the most probable finite-time Lyapunov exponent increases, meaning that the phase-space dynamics tends to be more ergodiclike. Our results suggest that the transport efficiency of interacting particles and heat conduction in periodic structures modeled by billiards will strongly be affected by the smoothness of physically realizable walls.