Kupferman R, Pavliotis G A, Stuart A M
Institute of Mathematics, The Hebrew University, Jerusalem 91904 Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Sep;70(3 Pt 2):036120. doi: 10.1103/PhysRevE.70.036120. Epub 2004 Sep 29.
We consider the dynamics of systems in the presence of inertia and colored multiplicative noise. We study the limit where the particle relaxation time and the correlation time of the noise both tend to zero. We show that the limiting equation for the particle position depends on the magnitude of the particle relaxation time relative to the noise correlation time. In particular, the limiting equation should be interpreted either in the Itô or Stratonovich sense, with a crossover occurring when the two fast-time scales are of comparable magnitude. At the crossover the limiting stochastic differential equation is neither of Itô nor of Stratonovich type. This means that, after adiabatic elimination, the governing equations have different drift fields, leading to different physical behavior depending on the relative magnitude of the two fast-time scales. Our findings are supported by numerical simulations.
我们考虑存在惯性和有色乘性噪声的系统动力学。我们研究粒子弛豫时间和噪声相关时间都趋于零的极限情况。我们表明，粒子位置的极限方程取决于粒子弛豫时间相对于噪声相关时间的大小。特别地，极限方程应根据伊藤或斯特拉托诺维奇意义来解释，当两个快时间尺度具有可比大小时会出现交叉。在交叉点处，极限随机微分方程既不是伊藤型也不是斯特拉托诺维奇型。这意味着，经过绝热消除后，控制方程具有不同的漂移场，导致根据两个快时间尺度的相对大小出现不同的物理行为。我们的发现得到了数值模拟的支持。
