Quantumness of discrete Hamiltonian cellular automata

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.

arXiv comment4 pages; invited talk at the symposium "Wigner 111 - Colourful and Deep" (Budapest, November 2013), to appear in EPJ Web of Conferences

References in corpus (3)

• Action principle for cellular automata and the linearity of quantum mechanics
• Assumptions that imply quantum dynamics is linear
• The Cellular Automaton Interpretation of Quantum Mechanics

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