  Finding equilibration times is a major unsolved problem in physics with few
analytical results. Here we look at equilibration times for quantum gases of
bosons and fermions in the regime of negligibly weak interactions, a setting
which not only includes paradigmatic systems such as gases confined to boxes,
but also Luttinger liquids and the free superfluid Hubbard model. To do this,
we focus on two classes of measurements: (i) coarse-grained observables, such
as the number of particles in a region of space, and (ii) few-mode
measurements, such as phase correlators and correlation functions. We show
that, in this setting, equilibration occurs quite generally despite the fact
that the particles are not interacting. Furthermore, for coarse-grained
measurements the timescale is generally at most polynomial in the number of
particles N, which is much faster than previous general upper bounds, which
were exponential in N. For local measurements on lattice systems, the timescale
is typically linear in the number of lattice sites. In fact, for one
dimensional lattices, the scaling is generally linear in the length of the
lattice, which is optimal. Additionally, we look at a few specific examples,
one of which consists of N fermions initially confined on one side of a
partition in a box. The partition is removed and the fermions equilibrate
extremely quickly in time O(1/N).
