Relativistic Open Quantum Systems II: Majorana particles

Relativistic states are much richer in features than those in non-relativity. One of the most important relativistic hallmarks is the ability to describe of antiparticles. We already know this from books of quantum mechanics, but it is in the phase space where we can visualize them in full glory.

Let us first watch the time-evolution of a free relativistic cat-state:

    This movie might as well describe a non-relativistic cat state, so, no surprise (the dynamics is undergoing quantum coherence).

Now, let us observe the evolution of the corresponding particle-antiparticle coherent superposition:

In this case we observe that the antiparticle at the bottom advances to the positive direction despite of having a negative momentum. This type of dynamics is characteristic of antiparticles!

One critical piece of information is that both states are undergoing the same degree of quantum decoherence due to the contact with an environment. Nevertheless, the particle-antiparticle superposition maintains the interference robust. We just found a state that belongs to a free-decoherence space!

Al should also mention that the relativistic state happens to be a Majorana state.

[1] Dirac open-quantum-system dynamics: Formulations and simulations,

Renan Cabrera, Andre G. Campos, Denys I. Bondar, and Herschel A. Rabitz Phys. Rev. A 94, 052111 – Published 14 November 2016