School of Mathematical & Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
8-2025
Abstract
The authors show that a large class of 2-adic Schrödinger equations is the scaling limit of certain continuous-time quantum Markov chains (CTQMCs). Practically, a discretization of such an equation gives a CTQMC. As a practical result, new types of continuous-time quantum walks (CTQWs) on graphs using two symmetric matrices are constructed. The transport between nodes in one direction is described by one matrix, while the transport between nodes in the opposite direction. This construction includes, as a particular case, the CTQWs constructed using adjacency matrices. The final goal of this work is to contribute to the understanding of the foundations of quantum mechanics (QM) and the role of the hypothesis of the discreteness of space. The connection between 2-adic QM and CTQWs shows that 2-adic QM has a physical meaning. 2-Adic QM is a nonlocal theory because the Hamiltonians used are nonlocal operators, and consequently, spooky actions at a distance are allowed. However, this theory is not a mathematical toy. The violation of Bell's inequality is experimentally confirmed, which implies that realism is allowed by this theory. The authors pointed out several new research problems connected with the foundations of QM.
Recommended Citation
Zúñiga‐Galindo, W. A. "2‐Adic Quantum Mechanics, Continuous‐Time Quantum Walks, and the Space Discreteness." Fortschritte der Physik 73, no. 8 (2025): e70019. https://doi.org/10.1002/prop.70019
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Title
Fortschritte der Physik
DOI
10.1002/prop.70019
Comments
© 2025 The Author(s). Fortschritte der Physik published by Wiley-VCH GmbH
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