The Dirac Quantum Cellular Automaton in one dimension: Zitterbewegung and scattering from potential

TL;DR

This paper analyzes a one-dimensional Dirac quantum cellular automaton, demonstrating how it reproduces key relativistic quantum phenomena like Zitterbewegung and Klein paradox, illustrating emergent particle behavior from quantum information processing.

Contribution

It provides analytical and simulation evidence that a quantum cellular automaton can emulate Dirac particle dynamics, including scattering and relativistic effects.

Findings

Automaton exhibits Zitterbewegung oscillations.

Automaton reproduces Klein paradox scattering.

Quantum information processing can mimic particle mechanics.

Abstract

We study the dynamical behaviour of the quantum cellular automaton of Refs. [1, 2], which reproduces the Dirac dynamics in the limit of small wavevectors and masses. We present analytical evaluations along with computer simulations, showing how the automaton exhibits typical Dirac dynamical features, as the Zitterbewegung and the scattering behaviour from potential that gives rise to the so-called Klein paradox. The motivation is to show concretely how pure processing of quantum information can lead to particle mechanics as an emergent feature, an issue that has been the focus of solid-state, optical and atomic-physics quantum simulator.