  We show that a closed quantum system driven through a quantum critical point
with two rates $\omega_1$ (which controls its proximity to the quantum critical
point) and $\omega_2$ (which controls the dispersion of the low-energy
quasiparticles at the critical point) exhibits novel scaling laws for defect
density $n$ and residual energy $Q$. We demonstrate suppression of both $n$ and
$Q$ with increasing $\omega_2$ leading to an alternate route to achieving
near-adiabaticity in a finite time for a quantum system during its passage
through a critical point. We provide an exact solution for such dynamics with
linear drive protocols applied to a class of integrable models, supplement this
solution with scaling arguments applicable to generic many-body Hamiltonians,
and discuss specific models and experimental systems where our theory may be
tested.
