We revisit here the problem of the collective non-equilibrium dynamics of a classical statistical system at a critical point and in the presence of surfaces. The effects of breaking separately space- and time-translational invariance are well understood, hence we focus here on the emergence of a non-trivial interplay between them. For this purpose, we consider a semi-infinite model with O(n)-symmetry and purely dissipative dynamics which is prepared in a disordered state and then suddenly quenched to its critical temperature. We determine the short-distance behaviour of its response function within a perturbative approach which does not rely on any a priori assumption on the scaling form of this quantity.
Marcuzzi, M., & Gambassi, A. (2014). Critical relaxation and the combined effects of spatial and temporal boundaries. Condensed Matter Physics, 17(3), Article 33603. https://doi.org/10.5488/CMP.17.33603