  Non-axisymmetric components, such as spirals and central bars, play a major
role in shaping galactic discs. An important aspect of the disc secular
evolution driven by these perturbers is the radial migration of stars. It has
been suggested recently that migration can populate a thick-disc component from
inner-disc stars with high vertical energies. Since this has never been
demonstrated in simulations, we study in detail the effect of radial migration
on the disc velocity dispersion and disc thickness, by separating simulated
stars into migrators and non-migrators. We apply this method to three isolated
barred Tree-SPH N-body galaxies with strong radial migration. Contrary to
expectations, we find that as stellar samples migrate, on the average, their
velocity dispersion change (by as much as 50%) in such a way as to
approximately match the non-migrating population at the radius at which they
arrive. We show that, in fact, migrators suppress heating in parts of the disc.
To confirm the validity of our findings, we also apply our technique to three
cosmological re-simulations, which use a completely different simulation scheme
and, remarkably, find very similar results. We believe the inability of
migration to thicken discs is a fundamental property of internal disc
evolution, irrespective of the migration mechanism at work. We explain this
with the approximate conservation of the (average) vertical and radial actions
rather than the energy. This "action mixing" can be used to constrain the
migration rate in the Milky Way: estimates of the average vertical action in
observations for different populations of stars should reveal flattening with
radius for older groups of stars.
