Editing Diffusion
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It follows from the previous equation that, for each of the Cartesian components, e.g. <math>x</math>: | It follows from the previous equation that, for each of the Cartesian components, e.g. <math>x</math>: | ||
:<math>D = \lim_{t \rightarrow \infty} \frac{1}{ | :<math>D = \lim_{t \rightarrow \infty} \frac{1}{2} \langle \vert x_i(t) \cdot x_i(0) \vert^2\rangle </math>, | ||
for every particle <math>i</math>. Therefore, an average over all particles can be employed in | for every particle <math>i</math>. Therefore, an average over all particles can be employed in | ||
order to improve statistics. The same applies to time averaging: in equilibrium the average | order to improve statistics. The same applies to time averaging: in equilibrium the average | ||
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so several time segments from the same simulation may be averaged for a given interval [2]. | so several time segments from the same simulation may be averaged for a given interval [2]. | ||
Adding all components, the following also applies: | Adding all components, the following also applies: | ||
:<math>D = \lim_{t \rightarrow \infty} \frac{1}{ | :<math>D = \lim_{t \rightarrow \infty} \frac{1}{6} \langle \vert \mathbf{r}_i(t) \cdot \mathbf{r}_i(0) \vert^2\rangle </math> | ||
==Green-Kubo relation== | ==Green-Kubo relation== |