Experiments with Schrödinger Cellular Automata
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918101975564288 |
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| author | van Berkel, Kees de Graaf, Jan van Hee, Kees |
| author_facet | van Berkel, Kees de Graaf, Jan van Hee, Kees |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08586 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Experiments with Schrödinger Cellular Automata van Berkel, Kees de Graaf, Jan van Hee, Kees Quantum Physics 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. |
| title | Experiments with Schrödinger Cellular Automata |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2406.08586 |