论文标题
在二维洛伦兹晶格气体中移动的粒子的动力学
Dynamics of a particle moving in a two dimensional Lorentz lattice gas
论文作者
论文摘要
我们研究在正方形的二维洛伦兹晶状体中移动的粒子的动力学。基础的晶格气体被两种旋转器占据：“右旋转器（R）”和“左旋转器（L）”，某些站点是空的{\ it {\ it {viz。}}空置空缺。$ r $和$ r $的密度和$ l $的密度相同，$ v $的密度是我们的密钥参数。旋转器确定性地将粒子速度向右或向左旋转，空缺使其保持不变。我们表征了不同空位的粒子运动动力学。由于系统是确定性的，因此粒子渐近地形成封闭的轨迹。在时间$ t $时，粒子处于封闭或开放轨迹中的概率是空缺密度的函数。 \ textColor {black} {粒子的运动是{\ it {rorform}}的整个晶格。然而，它在部分空置的晶格中分为两个不同的阶段}：运动的第一阶段，这是本研究的重点，其特征是异常扩散和一个处于开放轨迹的概率的幂律衰减。运动的第二阶段的特征是延伸运动和在开放轨迹中的概率的指数衰减。对于空位非零密度的晶格，随着空缺的密度的增加，运动的第一阶段持续更长的时间。
We study the dynamics of a particle moving in a square two-dimensional Lorentz lattice-gas. The underlying lattice-gas is occupied by two kinds of rotators, "right-rotator (R)" and "left-rotator (L)" and some of the sites are empty {\it{viz.}} vacancy "V".The density of $R$ and $L$ are the same and density of $V$ is one of the key parameters of our model. The rotators deterministically rotate the direction of a particle's velocity to the right or left and vacancies leave it unchanged. We characterise the dynamics of particle motion for different densities of vacancies. Since the system is deterministic, the particle forms a closed trajectory asymptotically. The probability of the particle being in a closed or open trajectory at time $t$ is a function of the density of vacancies. \textcolor{black}{The motion of the particle is {\it{uniform}} throughout in a fully occupied lattice. However, it is divided in two distinct phases in partially vacant lattices}: The first phase of the motion, which is the focus of this study, is characterised by anomalous diffusion and a power-law decay of the probability of being in an open trajectory. The second phase of the motion is characterised by subdiffusive motion and an exponential decay of the probability of being in an open trajectory. For lattices with a non-zero density of vacancies, the first phase of motion lasts for a longer period of time as the density of vacancies increases.
