Quantumness of discrete Hamiltonian cellular automata

Understand

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.