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Open Quantum Systems Decoherence
Quantum Simulation
Experiments with Schrödinger Cellular Automata
arXiv
Authors: Kees van Berkel, Jan de Graaf, Kees van Hee
Year
2024
Paper ID
66596
Status
Preprint
Abstract Read
~2 min
Abstract Words
86
Citations
N/A
Abstract
We derive a class of cellular automata for the Schrödinger 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.
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- This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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- We derive a class of cellular automata for the Schrödinger Hamiltonian, including scalar and vector potentials.
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