title: Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation.
abstract: We point out a formal analogy between the Dirac equation in Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. By a systematic analysis based on the theory of operator splitting, this analogy is shown to turn into a concrete and efficient computational method, providing a unified treatment of relativistic and nonrelativistic quantum mechanics. This might have potentially far-reaching implications for both classical and quantum computing, because it shows that, by splitting time along the three spatial directions, quantum information (Dirac-Majorana wave function) propagates in space-time as a classical statistical process (Boltzmann distribution).
authors.affiliation: Centre de Recherches Mathématiques, Université de Montréal, Montréal, Canada H3T 1J4.
authors.forename: F
authors.initials: F
authors.lastname: Fillion-Gourdeau
authors.forename: H J
authors.initials: HJ
authors.lastname: Herrmann
authors.forename: M
authors.initials: M
authors.lastname: Mendoza
authors.forename: S
authors.initials: S
authors.lastname: Palpacelli
authors.forename: S
authors.initials: S
authors.lastname: Succi