布朗粒子在无序关联势上的无偏扩散
Unbiased diffusion of Brownian particles on disordered correlated potentials
摘要：
在这项工作中，我们研究了非相互作用的过阻尼粒子的扩散，无偏无序相关势，受到高斯白噪声。我们得到一个精确的扩散系数的表达式，这使我们能够证明，无偏扩散的过阻尼粒子的随机聚合物不依赖于无序势的相关性。无偏扩散系数的这种普遍行为是爱因斯坦关系的有效性和无规聚合物的相关性衰减的直接结果。我们测试的相关性的两个不同的随机过程，一个一步马尔可夫链和扩展修改系统产生的相关聚合物的扩散系数的独立性。在我们的模拟的准确性，我们发现，这些系统的数值计算得到的扩散系数与解析计算的一致，证实了我们的预测。
英文摘要：
In this work we study the diffusion of non-interacting overdamped particles, moving on unbiased disordered correlated potentials, subjected to Gaussian white noise. We obtain an exact expression for the diffusion coefficient which allows us to prove that the unbiased diffusion of overdamped particles on a random polymer does not depend on the correlations of the disordered potentials. This universal behavior of the unbiased diffusivity is a direct consequence of the validity of the Einstein relation and the decay of correlations of the random polymer. We test the independence on correlations of the diffusion coefficient for correlated polymers produced by two different stochastic processes, a one-step Markov chain and the expansion-modification system. Within the accuracy of our simulations, we found that the numerically obtained diffusion coefficient for these systems agree with the analytically calculated ones, confirming our predictions.
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