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From generalized Langevin equations to Brownian dynamics and embedded Brownian dynamics

机译:从广义Langevin方程到布朗动力学和嵌入式布朗动力学

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摘要

We present the reduction of generalized Langevin equations to a coordinate-only stochastic model, which in its exact form involves a forcing term with memory and a general Gaussian noise. It will be shown that a similar fluctuation-dissipation theorem still holds at this level. We study the approximation by the typical Brownian dynamics as a first approximation. Our numerical test indicates how the intrinsic frequency of the kernel function influences the accuracy of this approximation. In the case when such an approximate is inadequate, further approximations can be derived by embedding the nonlocal model into an extended dynamics without memory. By imposing noises in the auxiliary variables, we show how the second fluctuation-dissipation theorem is still exactly satisfied. Published by AIP Publishing.
机译:我们提出将广义Langevin方程简化为仅坐标的随机模型,其精确形式涉及带有记忆的强迫项和一般的高斯噪声。可以证明,在这个水平上,仍然存在类似的波动耗散定理。我们以典型的布朗动力学作为第一近似来研究该近似。我们的数值测试表明核函数的固有频率如何影响这种近似的准确性。在这种近似不充分的情况下,可以通过将非局部模型嵌入到没有内存的扩展动态中来得出进一步的近似。通过在辅助变量中施加噪声,我们展示了如何仍然精确地满足第二个耗散定理。由AIP Publishing发布。

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