  We analyze the coherent quantum evolution of a many-particle system after
slowly sweeping a power-law confining potential. The amplitude of the confining
potential is varied in time along a power-law ramp such that the many-particle
system finally reaches or crosses a critical point. Under this protocol we
derive general scaling laws for the density of excitations created during the
non-adiabatic sweep of the confining potential. It is found that the mean
excitation density follows an algebraic law as a function of the sweeping rate
with an exponent that depends on the space-time properties of the potential. We
confirm our scaling laws by first order adiabatic calculation and exact results
on the Ising quantum chain with a varying transverse field.
