Nonlinear behavior of a many-body one-dimensional plasma sheet model and its transport phenomena

由均匀分布的正电荷中的负电荷片组成的一维等离子体片模型，等效为一个围绕平衡位置相互等距的简谐振子系统，相邻振子弹性碰撞。因此，如果用作用变量和角度变量来描述每个薄片的运动，那么作用变量就是运动的常量，在振子发生碰撞之前，运动是规则的。当相邻振子对发生碰撞时，由于相邻振子对之间的动量交换，它们的作用变量会发生不连续的跳跃。通过连接每次碰撞前后的解析解，可以进行数值计算。首先，我们通过施加不同温度的热浴的边界条件来研究该系统的导热系数，并计算了从一个边界到另一个边界的能量流。在低温下，电导系数的尺寸依赖关系是正常的。然而，在较高的温度下，该系数存在尺寸依赖性，这是由于在相空间中观察到的薄片的弹道运动所致。也就是说，势井中有弹道薄片(自由粒子运动)和囚禁薄片。在较低的温度下，速度的麦克斯韦分布趋势较快，轨道的不稳定性由于混沌而增强。我们成功地用逃逸率公式解释了这些行为，这意味着格林-久保公式至少在低温下是有效的。为了理解这些观测，我们现在正在发展一个基于作用变量和角度变量的动力学理论，用于角度变量的分布函数的演化。我们还研究了粒子输运(扩散)对非线性化学反应的影响，这可能在非平衡条件下产生空间关联，

A one-dimenslonal plasma sheet model, which consists of negatively charged sheets in a uniformly distributed positive charges, is equivalent to a system of harmonic oscillators around equilibrium positions equally separated from each other, neighboring oscillators colliding elastically. Therefore, if the motion of each sheet is described in terms of action and angle variables, the action variables are constants of motion and the motion is regular until collision of oscillators occurs. When collisionof neighboring pair of oscillators, their action variables undergo discontinuous jumps due to exchange of momenta between neighboring pair. Numerical calculation can be done by connecting analytical solutions before and after each collision. First, we investigated thermal conductivity of this system by imposing boundary condition of heat baths of different temperatures and calculate energyflow from one boundary to the other. The size dependence of the conductivity coefficient is normal as long as the system is at low temperature. However, at higher temperature, there is size-dependence of the coefficient, which is due to ballistic motion of sheets as observed in the phase space. Namely there are ballistic sheets(free particle motion) and trapped sheets in potential wells. The tendencyto Maxwell distribution of velocities is quick at lower temperature, where orbital instability is enhanced due to chaos. We succeeded to explain these behavior by the usage of escape rate formalism which implies that Green-Kubo formula works at least at low temperature. In order to under stand these observations, we are now developing a kinetic theory based up on action and angle variables for the evolution of distribution function of angle variables. We have also investigated effect of particle transport (diffusion) on non-linear chemical reaction, which may create spatial correlation under nonequilibrium conditions,