  We present an analysis of the structure of post-starburst (PSB) galaxies in
the redshift range $0.5 < z < 2$, using a photometrically-selected sample
identified in the Ultra Deep Survey (UDS) field. We examine the structure of
$\sim80$ of these transient galaxies using radial light $\mu(r)$ profiles
obtained from CANDELS $\textit{Hubble Space Telescope}$ near-infrared/optical
imaging, and compare to a large sample of $\sim2000$ passive and star-forming
galaxies. For each population, we determine their typical structural properties
(effective radius $r_{\rm e}$, S\'ersic index $n$) and find significant
differences in PSB structure at different epochs. At high redshift ($z > 1$),
PSBs are typically massive ($M_* > 10^{10}\rm\,M_{\odot}$), very compact and
exhibit high S\'ersic indices, with structures that differ significantly from
their star-forming progenitors but are similar to massive passive galaxies. In
contrast, at lower redshift ($0.5 < z < 1$), PSBs are generally of low mass
($M_* < 10^{10}\rm\,M_{\odot}$) and exhibit compact but less concentrated
profiles (i.e. lower S\'ersic indices), with structures similar to low-mass
passive discs. Furthermore, for both epochs we find remarkably consistent PSB
structure across the optical/near-infrared wavebands (which largely trace
different stellar populations), suggesting that any preceding starburst and/or
quenching in PSBs was not strongly centralized. Taken together, these results
imply that PSBs at $z > 1$ have been recently quenched during a major
disruptive event (e.g. merger or protogalactic collapse) which formed a compact
remnant, while at $z < 1$ an alternative less disruptive process is primarily
responsible. Our results suggest that high-$z$ PSBs are an intrinsically
different population to those at lower redshifts, and indicate different
quenching routes are active at different epochs.
