Condensed Matter Physics, 2014, vol. 17, No. 3, p. 33603:1-14
Critical relaxation and the combined effects of spatial and temporal boundaries
(SISSA - International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy; School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, UK)
(SISSA --- International School for Advanced Studies and INFN, via Bonomea 265, 34136 Trieste, Italy)
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.
stochastic dynamics, boundary field theory
64.60.De, 64.60.Ht, 68.35.Rh