  We investigate the wave packet dynamics of a pair of particles that undergoes
a rapid change of scattering length. The short-range interactions are modeled
in the zero-range limit, where the quench is accomplished by switching the
boundary condition of the wave function at vanishing particle separation. This
generates a correlation wave that propagates rapidly to nonzero particle
separations. We have derived universal, analytic results for this process that
lead to a simple phase-space picture of the quench-induced scattering.
Intuitively, the strength of the correlation wave relates to the initial
contact of the system. We find that, in one spatial dimension, the $k^{-4}$
tail of the momentum distribution contains a ballistic contribution that does
not originate from short-range pair correlations, and a similar conclusion can
hold in other dimensionalities depending on the quench protocol. We examine the
resultant quench-induced transport in an optical lattice in 1D, and a
semiclassical treatment is found to give quantitatively accurate estimates for
the transport probabilities.
