  In many quantum quench experiments involving cold atom systems the
post-quench system can be described by a quantum field theory of free scalars
or fermions, typically in a box or in an external potential. We work with free
scalars in arbitrary dimensions generalizing the techniques employed in our
earlier work \cite{Mandal:2015kxi} in 1+1 dimensions. In this paper, we
generalize to $d$ spatial dimensions for arbitrary $d$. The system is
considered in a box much larger than any other scale of interest. We start with
the ground state, or a squeezed state, with a high mass and suddenly quench the
system to zero mass ("critical quench"). We explicitly compute time-dependence
of local correlators and show that at long times they are described by a
generalized Gibbs ensemble (GGE), which, in special cases, reduce to a thermal
(Gibbs) ensemble. The equilibration of {\it local} correlators can be regarded
as `subsystem thermalization' which we simply call 'thermalization' here (the
notion of thermalization here also includes equlibration to GGE). The rate of
approach to equilibrium is exponential or power law depending on whether $d$ is
odd or even respectively. As in 1+1 dimensions, details of the quench protocol
affect the long time behaviour; this underlines the importance of irrelevant
operators at IR in non-equilibrium situations. We also discuss quenches from a
high mass to a lower non-zero mass, and find that in this case the approach to
equilibrium is given by a power law in time, for all spatial dimensions $d$,
even or odd.
