Schrödinger细胞自动机实验

IF 5.1 2区物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY

Quantum Pub Date : 2025-07-23 DOI:10.22331/q-2025-07-23-1811

Kees van Berkel, Jan de Graaf, Kees van Hee

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引用次数: 0

摘要

我们导出了一类元胞自动机的Schrödinger哈密顿量，包括标量势和矢量势。它基于哈密顿算子的多次分裂，得到离散时间和空间中的多步酉演化算子。一维自动机的实验提供了对相速度和群速度、能级、相关近似误差和随时间变化的谐波振荡器演化的定量见解。空间波形混叠的明显影响是有趣的。二维自动机干涉实验包括折射、davison - germer、Mach-Zehnder、单一&；双缝和阿哈罗诺夫-博姆。

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Experiments with Schrödinger Cellular Automata

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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来源期刊

Quantum Physics and Astronomy-Physics and Astronomy (miscellaneous)

CiteScore

9.20

自引率

10.90%

发文量

241

审稿时长

16 weeks

期刊介绍： Quantum is an open-access peer-reviewed journal for quantum science and related fields. Quantum is non-profit and community-run: an effort by researchers and for researchers to make science more open and publishing more transparent and efficient.