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Sub-Compton quantum non-equilibrium and Majorana systems

We study the Majorana equation from the point of view of the de Broglie-Bohm pilot-wave theory (according to which a quantum ensemble of fermions is not only described by a spinor but also by a distribution of position configurations). Although the Majorana equation involves a mass parameter, we show that the positions undergo luminal motion. In the case of free systems, we also show that the trajectory can be strongly helical (the diameter of the helix being the Compton wavelength). On a coarse-grained level (coarse-graining with respect to the Compton wavelength), these trajectories appear subluminal. The peculiar nature of the Majorana trajectory suggests a study of the temporal evolution of quantum non-equilibrium distributions, which are distributions allowed in the pilot-wave theory, in which the configurations are not distributed according to Born's law. We do such simulations for Dirac and Majorana systems, and we investigate whether quantum non-equilibrium might survive at the sub-Compton scale in systems described by Majorana spinors.