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

一维等离子体片模型是由均匀分布的正电荷中的负电荷片组成的，它等价于一个谐振子系统，谐振子围绕平衡位置等距分布，相邻的谐振子弹性碰撞。因此，如果用作用变量和角度变量来描述每个薄片的运动，则作用变量是运动常数，并且运动是规则的，直到振子发生碰撞。当相邻振子对碰撞时，由于相邻振子对之间的动量交换，它们的作用量发生不连续的跳跃。数值计算可以通过连接每次碰撞前后的解析解来完成。首先，我们通过施加不同温度的热浴边界条件来研究该系统的热导率，并计算从一个边界到另一个边界的能量流。只要系统处于低温，电导系数的尺寸依赖性是正常的。然而，在较高的温度下，有尺寸依赖性的系数，这是由于在相空间中观察到的片的弹道运动。即在势威尔斯中存在着弹道层（自由粒子运动）和俘获层。在较低温度下，速度向麦克斯韦分布的趋势较快，混沌使轨道不稳定性增强。我们成功地解释了这些行为的逃逸率形式主义的使用，这意味着格林-久保公式至少在低温下工作。为了理解这些观测结果，我们现在正在发展一种基于作用量和角度变量的动力学理论，用于角度变量分布函数的演化。我们还研究了粒子输运（扩散）对非线性化学反应的影响，这可能会在非平衡条件下产生空间相关性，

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,