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Collisions of actinide nuclei form, during very short times of few zs($10^{-21}$ s), the heaviest ensembles of interacting nucleons available onEarth. Such collisions are used to produce super-strong electric fields by thehuge number of interacting protons to test spontaneous positron-electron pairemission (vacuum decay) predicted by the quantum electrodynamics (QED) theory.Multi-nucleon transfer in actinide collisions could also be used as analternative way to fusion in order to produce neutron-rich heavy and superheavyelements thanks to inverse quasifission mechanisms. Actinide collisions arestudied in a dynamical quantum microscopic approach. The three-dimensionaltime-dependent Hartree-Fock (TDHF) code {\textsc{tdhf3d}} is used with a fullSkyrme energy density functional to investigate the time evolution ofexpectation values of one-body operators, such as fragment position andparticle number. This code is also used to compute the dispersion of theparticle numbers (e.g., widths of fragment mass and charge distributions) fromTDHF transfer probabilities, on the one hand, and using the Balian-Veneronivariational principle, on the other hand. A first application to test QED isdiscussed. Collision times in $^{238}$U+$^{238}$U are computed to determine theoptimum energy for the observation of the vacuum decay. It is shown that theinitial orientation strongly affects the collision times and reactionmechanism. The highest collision times predicted by TDHF in this reaction areof the order of $\sim4$ zs at a center of mass energy of 1200 MeV. According tomodern calculations based on the Dirac equation, the collision times at$E_{cm}>1$ GeV are sufficient to allow spontaneous electron-positron pairemission from QED vacuum decay, in case of bare uranium ion collision. A secondapplication of actinide collisions to produce neutron-rich transfermiums isdiscussed. A new inverse quasifission mechanism associated to a specificorientation 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 anucleon flux toward the latter. The probability distributions for transfermiumproduction in such a collision are computed. The produced nuclei are moreneutron-rich than those formed in fusion reactions, thus, leading to morestable isotopes closer to the predicted superheavy island of stability. Inaddition to mass and charge dispersion, the Balian-Veneroni variationalprinciple is used to compute correlations between $Z$ and $N$ distributions,which are zero in standard TDHF calculations.

Actinide collisions for QED and superheavy elements with the time-dependent Hartree-Fock theory and the Balian-V\'en\'eroni variational principle