  The first large-scale quantum mechanical simulations of pulsar glitches are
presented, using a Gross-Pitaevskii model of the crust-superfluid system in the
presence of pinning. Power-law distributions of simulated glitch sizes are
obtained, in accord with astronomical observations, with exponents ranging from
-0.55 to -1.26. Examples of large-scale simulations, containing $\sim 200$
vortices, reveal that these statistics persist in the many-vortex limit.
Waiting-time distributions are also constructed. These and other statistics
support the hypothesis that catastrophic unpinning mediated by collective
vortex motion produces glitches; indeed, such collective events are seen in
time-lapse movies of superfluid density. Three principal trends are observed.
(1) The glitch rate scales proportional to the electromagnetic spin-down
torque. (2) A strong positive correlation is found between the strength of
vortex pinning and mean glitch size. (3) The spin-down dynamics depend less on
the pinning site abundance once the latter exceeds one site per vortex,
suggesting that unpinned vortices travel a distance comparable to the
inter-vortex spacing before repinning.
