Gauthier Michel G, Slater Gary W
Department of Physics, University of Ottawa, 150 Louis-Pasteur, Ottawa, Ontario, Canada.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004;70(1 Pt 2):015103. doi: 10.1103/PhysRevE.70.015103. Epub 2004 Jul 26.
We revisit the well-known issue of representing an overdamped drift-and-diffusion system by an equivalent lattice random-walk model. We demonstrate that commonly used Monte Carlo algorithms do not conserve the diffusion coefficient when a driving field of arbitrary amplitude is present, and that such algorithms would actually require fluctuating jumping times and one clock per Cartesian direction to work properly. Although it is in principle possible to construct valid algorithms with fixed time steps, we show that no such algorithm can be used in more than two dimensions if the jumps are made along only one axis at each time step.
我们重新审视了用等效晶格随机游走模型表示过阻尼漂移扩散系统这一著名问题。我们证明，当存在任意幅度的驱动场时，常用的蒙特卡罗算法无法守恒扩散系数，并且此类算法实际上需要波动的跳跃时间以及每个笛卡尔方向一个时钟才能正常工作。尽管原则上有可能构建具有固定时间步长的有效算法，但我们表明，如果每次时间步仅沿一个轴进行跳跃，那么在超过二维的情况下无法使用此类算法。
