Quantumness of discrete Hamiltonian cellular automata
Quantum Physics
2014-10-13 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger equation. This allows to construct an invertible map between such CA and continuous quantum mechanical models, which incorporate a fundamental scale. Presently, we emphasize general aspects of these findings, the construction of admissible CA observables, and the existence of solutions of the modified dispersion relation for stationary states.
Keywords
Cite
@article{arxiv.1407.2160,
title = {Quantumness of discrete Hamiltonian cellular automata},
author = {Hans-Thomas Elze},
journal= {arXiv preprint arXiv:1407.2160},
year = {2014}
}
Comments
4 pages; invited talk at the symposium "Wigner 111 - Colourful and Deep" (Budapest, November 2013), to appear in EPJ Web of Conferences