In the notation of Section 15.3, show that for a Brownian particle [ langleboldsymbol{v}(t) cdot boldsymbol{F}(t)angle=3 k
Question:
In the notation of Section 15.3, show that for a Brownian particle
\[
\langle\boldsymbol{v}(t) \cdot \boldsymbol{F}(t)angle=3 k T / \tau, \quad \text { while }\langle\boldsymbol{v}(t) \cdot \mathcal{F}(t)angle=0
\]
On the other hand,
\[
\langle\boldsymbol{r}(t) \cdot \mathcal{F}(t)angle=-3 k T, \quad \text { while }\langle\boldsymbol{r}(t) \cdot \boldsymbol{F}(t)angle=0 .
\]
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By eqn 1532 we have langlemathbfv cdot mathbfFangleMleftlanglemathbfv cdot fracd mathbfvd t ightangl...View the full answer
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