论文标题
在边缘形屏障上的空间扩散的Kramers问题的数值解决方案的两种方法
Two ways for numerical solution of the Kramers problem for spatial diffusion over an edge-shaped barrier
论文作者
论文摘要
通过计算机建模研究了高耗散处的边缘形屏障上的热衰减速率。应用了两种随机Langevin类型方程：（i）坐标和共轭动量的langevin方程（LEQP，相空间扩散），以及（ii）降低的langevin方程（RLE，空间扩散，过度阻尼运动）。后一种方法更快，相似。但是，人们在具有不连续力的边缘形屏障的情况下会怀疑其适用性。原因是，由于屏障处的电位曲线的曲率等于无穷大，因此无法实现RLE适用性的形式条件。目前的数值研究表明，对于大摩擦，使用RLE计算的衰减速率与更精确的LEQP产生的速率一致。此外，事实证明，吸收边界位置的影响与文献中已知的谐波潜力相似。
Thermal decay rate over an edge-shaped barrier at high dissipation is studied numerically through the computer modeling. Two sorts of the stochastic Langevin type equations are applied: (i) the Langevin equations for the coordinate and conjugate momentum (LEqp, the phase space diffusion) and (ii) the reduced Langevin equation (RLE, the spatial diffusion, overdamped motion). The latter method is much faster and self-similar; however, one can doubt about its applicability in the case of an edge-shaped barrier with a discontinuous force. The reason is that a formal condition of the applicability of the RLE is not fulfilled since the curvature of the potential profile at the barrier is equal to infinity. The present numerical study demonstrates that, for large friction, the decay rate calculated using the RLE agrees with the rate resulting from the more exact LEqp. Moreover, it turns out that the influence of the position of the absorbing border is similar to the case of harmonic potential known in the literature.
