  Collisions of actinide nuclei form, during very short times of few zs
($10^{-21}$ s), the heaviest ensembles of interacting nucleons available on
Earth. Such collisions are used to produce super-strong electric fields by the
huge number of interacting protons to test spontaneous positron-electron pair
emission (vacuum decay) predicted by the quantum electrodynamics (QED) theory.
Multi-nucleon transfer in actinide collisions could also be used as an
alternative way to fusion in order to produce neutron-rich heavy and superheavy
elements thanks to inverse quasifission mechanisms. Actinide collisions are
studied in a dynamical quantum microscopic approach. The three-dimensional
time-dependent Hartree-Fock (TDHF) code {\textsc{tdhf3d}} is used with a full
Skyrme energy density functional to investigate the time evolution of
expectation values of one-body operators, such as fragment position and
particle number. This code is also used to compute the dispersion of the
particle numbers (e.g., widths of fragment mass and charge distributions) from
TDHF transfer probabilities, on the one hand, and using the Balian-Veneroni
variational principle, on the other hand. A first application to test QED is
discussed. Collision times in $^{238}$U+$^{238}$U are computed to determine the
optimum energy for the observation of the vacuum decay. It is shown that the
initial orientation strongly affects the collision times and reaction
mechanism. The highest collision times predicted by TDHF in this reaction are
of the order of $\sim4$ zs at a center of mass energy of 1200 MeV. According to
modern calculations based on the Dirac equation, the collision times at
$E_{cm}>1$ GeV are sufficient to allow spontaneous electron-positron pair
emission from QED vacuum decay, in case of bare uranium ion collision. A second
application of actinide collisions to produce neutron-rich transfermiums is
discussed. A new inverse quasifission mechanism associated to a specific
orientation of the nuclei is proposed to produce transfermium nuclei ($Z>100$)
in the collision of prolate deformed actinides such as $^{232}$Th+$^{250}$Cf.
The collision of the tip of one nucleus with the side of the other results in a
nucleon flux toward the latter. The probability distributions for transfermium
production in such a collision are computed. The produced nuclei are more
neutron-rich than those formed in fusion reactions, thus, leading to more
stable isotopes closer to the predicted superheavy island of stability. In
addition to mass and charge dispersion, the Balian-Veneroni variational
principle is used to compute correlations between $Z$ and $N$ distributions,
which are zero in standard TDHF calculations.
