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authoraristote <quentin.aristote@irif.fr>2025-07-26 23:38:08 +0200
committeraristote <quentin.aristote@irif.fr>2025-07-26 23:38:08 +0200
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parentee18dbf2546c3374abcf5a63942b777fd46eb23f (diff)
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+---
+references:
+- id: aristoteDynamicalTriangulationInduced2020
+ abstract: >-
+ 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 exp(a log(t) -
+ bt²), where a and b 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.
+ accessed:
+ - year: 2020
+ month: 8
+ day: 17
+ author:
+ - family: Aristote
+ given: Quentin
+ - family: Eon
+ given: Nathanaël
+ - family: Molfetta
+ given: Giuseppe
+ non-dropping-particle: di
+ citation-key: aristoteDynamicalTriangulationInduced2020
+ container-title: Symmetry
+ DOI: 10.3390/sym12010128
+ ISSN: 2073-8994
+ issue: '1:128'
+ issued:
+ - year: 2020
+ month: 1
+ language: en
+ license: http://creativecommons.org/licenses/by/3.0/
+ number: '1'
+ publisher: Multidisciplinary Digital Publishing Institute
+ title: Dynamical Triangulation Induced by Quantum Walk
+ type: article-journal
+ URL: https://www.mdpi.com/2073-8994/12/1/128
+ volume: '12'
+...