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We compute the average squared distance, $s^2(t)$, travelled by alight-flavour off-mass-shell coloured parton in a strongly-coupled$\mathcal{N}=4$ $SU(N_c)$ super-symmetric Yang Mills plasma using thegauge/string duality. In fact, we derive a closed integral expression for$s^2(t;a)$ in $AdS_3$-Schwarzschild, which interpolates between a heavy quarkwhen $a = 0$ and a light quark when $a = 1$, that we evaluate analytically forsmall virtualities - labelled $s_\text{small}^2(t;a)$. For arbitraryvirtualities, we show that for asymptotically early times the motion isballistic, $\left.s^2(t;a)\right|_{t\ll\beta}\sim t^2$, while at asymptoticallylate times the motion is diffusive, $\left. s^2(t;a) \right|_{t\gg\beta} =s_\text{small}^2(t;a) \sim 2D(a) t$, from which we are able to extract thediffusion coefficient $D(a)$. Motivated by the apparent universality of thelate time behaviour, we compute $s_{\text{small}}^2(t;a,d)$ and $D(a,d)$ for anarbitrary $AdS_d$-Schwarzschild geometry. From $D(a,d)$ we then compute for thefirst time the dynamic, time-dependent transverse momentum squared per unitpath length picked up by a high momentum light quark in a strongly-coupledplasma, the transport coefficient $\hat{q}(t)$, which is critically importantfor phenomenology in heavy ion collisions.

A semi-classical recipe for wobbly limp noodles in partonic soup