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Open AccessArticle

Dynamical Triangulation Induced by Quantum Walk

1
Aix-Marseille Université, Université de Toulon, CNRS, LIS, 13397 Marseille, France
2
École Normale Supérieure, PSL University, 75005 Paris, France
*
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(1), 128; https://doi.org/10.3390/sym12010128
Received: 17 December 2019 / Revised: 31 December 2019 / Accepted: 4 January 2020 / Published: 8 January 2020
(This article belongs to the Special Issue The Quantum Simulation of Everything (and Beyond))
We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated 2 - manifold. The triangulation is changed through Pachner moves, induced by the walker density itself, allowing the surface to transform into any topologically equivalent one. This model extends the quantum walk over triangular grid, introduced in a previous work, by one of the authors, whose space-time limit recovers the Dirac equation in (2+1)-dimensions. Numerical simulations show that the number of triangles and the local curvature grow as t α e β t 2 , where α and β parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Finally, we also prove that the global behavior of the walker, remains the same under spacetime random fluctuations. View Full-Text
Keywords: discrete time dynamical system; quantum walk; Pachner moves; dynamical triangulation; general relativity discrete time dynamical system; quantum walk; Pachner moves; dynamical triangulation; general relativity
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Aristote, Q.; Eon, N.; Di Molfetta, G. Dynamical Triangulation Induced by Quantum Walk. Symmetry 2020, 12, 128.

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