Quantumness of discrete Hamiltonian cellular automata
arXiv:1407.2160 · doi:10.1051/epjconf/20147802005
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 Schrödinger 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.
4 pages; invited talk at the symposium "Wigner 111 - Colourful and Deep" (Budapest, November 2013), to appear in EPJ Web of Conferences