= Solution
A creep experiment applies a small step of <stress> and holds it constant while recording <strain>. For $\sigma=\sigma_0H(t)$, the series <spring> jumps by $\sigma_0/G_0$ and the <dashpot> subsequently flows at constant rate $\sigma_0/\eta$. The <creep compliance> is thus
$$
J(t)=\frac{\epsilon(t)}{\sigma_0}=\frac1{G_0}+\frac t\eta,\qquad t>0.
$$
Using the stipulated effective <stress> and <strain> substitutions gives
$$
\frac{\langle r^2(t)\rangle}{a^2}
=\frac{k_BT}{\pi a^3}\left(\frac1{G_0}+\frac t\eta\right),
\qquad
\boxed{\langle r^2(t)\rangle_{\rm model}=\frac{k_BT}{\pi aG_0}+\frac{k_BT}{\pi a\eta}\,t.}
$$
On linear axes the model is a straight line of positive intercept $A=k_BT/(\pi aG_0)$ and slope $A/\tau$. On logarithmic axes it has an approximate elastic plateau for $t\ll\tau$ and slope one for $t\gg\tau$, within the <time> window where the continuum approximation applies. The long-time slope is $6D$ with $D=k_BT/(6\pi\eta a)$, agreeing with the <Stokes–Einstein relation>.
There is an essential zero-lag convention. A literal lag <displacement> $\Delta\mathbf r(t)=\mathbf r(t_0+t)-\mathbf r(t_0)$ has $\langle|\Delta\mathbf r(0)|^2\rangle=0$. The nonzero intercept above is the spring-compliance extrapolation of the idealized <microrheology of a Maxwell fluid>, after unresolved solvent or inertial transients. It must not be interpreted as an instantaneous finite physical <displacement> at exactly zero lag. The stated mesh condition motivates a continuum probe response; quantitative use is more reliable for $a\gg m$ than merely $a>m$.
\Image[/past-exam-of-the-soft-condensed-matter-course-of-the-university-of-cambridge/2012/paper-1-maxwell-creep.png]
{title=Maxwell probe displacement}
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