---
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'
...