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arXiv · 1310.0686

Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation

F. Fillion-Gourdeau·H. J. Herrmann·M. Mendoza·S. Palpacelli·S. Succi
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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 non-relativistic 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 wavefunction) propagates in space-time as a classical statistical process (Boltzmann distribution).

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F. Fillion-Gourdeau, H. J. Herrmann, M. Mendoza, S. Palpacelli, S. Succi. 2013-10-02. Formal analogy between the Dirac equation in its Majorana form and the discrete-velocity version of the Boltzmann kinetic equation. https://doi.org/10.1103/physrevlett.111.160602

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