Kees van Hee | Searcharxiv

arXiv2024

Experiments with Schr\"odinger Cellular Automata

We derive a class of cellular automata for the Schr\"odinger Hamiltonian, including scalar and vector potentials. It is based on a multi-split of the Hamiltonian, resulting in a multi-step unitary evolution operator in discrete time and space. Experiments with one-dimensional automata offer quantitative insight in phase and group velocities, energy levels, related approximation errors, and the evolution of a time-dependent harmonic oscilator. The apparent effects of spatial waveform aliasing are intriguing. Interference experiments with two-dimensional automata include refraction, Davisson-Germer, Mach-Zehnder, single & double slit, and Aharonov-Bohm.

quant-ph↗

arXiv2023

A Appropriate Probability Model for the Bell Experiment

The Bell inequality constrains the outcomes of measurements on pairs of distant entangled particles. The Bell contradiction states that the Bell inequality is inconsistent with the calculated outcomes of these quantum experiments. This contradiction led many to question the underlying assumptions, viz. so-called realism and locality. The probability model underlying the Bell inequality is generally left implicit. We propose an explicit probability model for the CHSH version of the Bell experiment. This model has only two simultaneously observable detector settings per measurement, and therefore does not assume realism. The quantum expectation now becomes a conditional expectation, given the two detector settings. This probability model is in full agreement with both quantum mechanics and experiments. As a result, the model satisfies the Bell inequality; there are no so-called violations. We extend this model to include a hidden variable. This extended model is not Bell-separable. This non-separability implies that the model is non-deterministic or non-local (or both).

quant-ph↗