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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'
...
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