论文标题
西奈模型中Ultraslow扩散的局部平衡特性
Local equilibrium properties of ultraslow diffusion in the Sinai model
论文作者
论文摘要
我们对随机淬灭的力场（称为西奈模型）中的热驱动，过度阻尼粒子进行数值研究。我们将无限的1维域上的无界运动与有限域中的运动进行了比较，并反映了边界，并表明无界运动的每一次都接近有限的增长尺寸的有限系统的平衡状态。这是由于时间尺度的分离而引起的：随机电势的内部井，存在相对较快的平衡，而跨主要潜在障碍的运动是Ultraslow。我们研究的数量是时间依赖的平均平方位移，粒子集合的时间依赖性平均能量以及概率分布的时间依赖性熵。使用非常快速的数值算法，我们可以探索时代的$ 10^{17} $步骤，从而研究有限的时间交叉现象。
We perform numerical studies of a thermally driven, overdamped particle in a random quenched force field, known as the Sinai model. We compare the unbounded motion on an infinite 1-dimensional domain to the motion in bounded domains with reflecting boundaries and show that the unbounded motion is at every time close to the equilibrium state of a finite system of growing size. This is due to time scale separation: Inside wells of the random potential, there is relatively fast equilibration, while the motion across major potential barriers is ultraslow. Quantities studied by us are the time dependent mean squared displacement, the time dependent mean energy of an ensemble of particles, and the time dependent entropy of the probability distribution. Using a very fast numerical algorithm, we can explore times up top $10^{17}$ steps and thereby also study finite-time crossover phenomena.
