  We present results on quantum quenches in systems with a fixed number of
particles in a large region. We show that the typical differences between local
and global quenches present in systems with regular thermodynamic limit are
lacking in this low-density limit. In particular, we show that in this limit
local quenches may not lead to equilibration to the new ground state, and that
global quenches can have power-law work distributions ("edge singularities")
typically associated with local quenches for finite-density systems. We also
show that this regime allows for large edge singularity exponents beyond that
allowed by the constraints of the usual thermodynamic limit. This
large-exponent singularity has observable consequences in the time evolution,
leading to a distinct intermediate power-law regime in time. We demonstrate
these results first using local quantum quenches in a low-density Kondo-like
system, and additionally through global and local quenches in Bose-Hubbard,
Aubry-Andre, and hard-core boson systems in the low-density regime.
