  We investigate the statistics of the work performed during a quench across a
quantum phase transition using the adiabatic perturbation theory. It is shown
that all the cumulants of work exhibit universal scaling behavior analogous to
the Kibble-Zurek scaling for the average density of defects. Two kinds of
transformations are considered: quenches between two gapped phases in which a
critical point is traversed, and quenches that end near the critical point. In
contrast to the scaling behavior of the density of defects, the scaling
behavior of the work cumulants are shown to be qualitatively different for
these two kinds of quenches. However, in both cases the corresponding exponents
are fully determined by the dimension of the system and the critical exponents
of the transition, as in the traditional Kibble-Zurek mechanism (KZM). Thus,
our study deepens our understanding about the nonequilibrium dynamics of a
quantum phase transition by revealing the imprint of the KZM on the work
statistics.
