论文标题
一个和二维的主动随机步行
Active Random Walks in One and Two Dimensions
论文作者
论文摘要
我们研究了主动的晶格步道：偏见的连续时间随机步道，这些步道在一个和两个空间尺寸的晶格方向之间执行定向扩散。我们在一个和二维上研究了晶格上任意位点的职业概率，并获得了连续限制的精确结果。接下来，我们在一个和二维中计算大偏差的自由能函数，我们用来在后期准确计算位移的矩和累积物。我们的确切结果表明，在大偏差函数中，$ x $和$ y $方向的运动之间的互相关持续存在。我们还证明，具有扩散的活动粒子的较大偏差函数显示了两个方案，具有不同的扩散行为。我们通过在一个和二维中的活性晶格助行器的动力学蒙特卡洛模拟来验证我们的分析结果。
We investigate active lattice walks: biased continuous time random walks which perform orientational diffusion between lattice directions in one and two spatial dimensions. We study the occupation probability of an arbitrary site on the lattice in one and two dimensions, and derive exact results in the continuum limit. Next, we compute the large deviation free energy function in both one and two dimensions, which we use to compute the moments and the cumulants of the displacements exactly at late times. Our exact results demonstrate that the cross-correlations between the motion in the $x$ and $y$ directions in two dimensions persist in the large deviation function. We also demonstrate that the large deviation function of an active particle with diffusion displays two regimes, with differing diffusive behaviors. We verify our analytic results with kinetic Monte Carlo simulations of an active lattice walker in one and two dimensions.
