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Vortex-Enhanced Zitterbewegung: Amplification Feasibility for Trapped-Ion Dirac Simulators

Rowan Brad Quni-Gudzinas

Published Jul 6, 2026• 0 citations
Publisher

Abstract

Assessment of whether the vortex-enhanced Zitterbewegung mechanism proposed by Guo, Xu & Gu (2025, arXiv:2511.21142) can amplify the sub-Compton-scale ZBW signal to experimentally detectable levels in trapped-ion Dirac simulators. Integrates the Predin (2026) areal-rate observable and the p-adic readout framework of the Adelic Physics Program (Quni 2026, P1/P3/P7).

DOI
10.5281/zenodo.21221898

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The Adelic Physics Program: A Grand Synthesis

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Six papers, one thesis: **Physics is adelic.** The Archimedean (real-number) description is the $\infty$-place readout of a richer ultrametric structure defined over the p-adic completions of $\mathbb{Q}$. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as $\mathbb{R}$ and $\mathbb{Q}_p$ for each prime $p$ — is the hidden organizing principle behind quantum measurement, quantum error correction, and the structure of spacetime at the Compton scale. We present the unified framework: Zitterbewegung (ZBW) is the physical manifestation of the p-adic channel of the adelic Dirac equation; Majorana zero modes are Bruhat-Tits fixed points encoding adelic topological charge; and adelic quantum error correction replaces active QEC codes with number-theoretic protection. This synthesis paper connects all six companion publications into a coherent research program with specific, falsifiable predictions. **Keywords:** Adelic physics, Ostrowski's theorem, Zitterbewegung, Bruhat-Tits tree, p-adic quantum mechanics, topological quantum computing, grand synthesis ---

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Assessment of whether the vortex-enhanced Zitterbewegung mechanism proposed by Guo, Xu & Gu (2025, arXiv:2511.21142) can amplify the sub-Compton-scale ZBW signal to experimentally detectable levels in trapped-ion Dirac simulators. Integrates the Predin (2026) areal-rate observable and the p-adic readout framework of the Adelic Physics Program (Quni 2026, P1/P3/P7).
Zitterbewegung (ZBW), the trembling motion predicted by the Dirac equation, has long remained unobservable in free electrons due to its sub-Compton scale. We elaborately construct a relativistic vortex electron wave packet as a coherent superposition of both positive- and negative-energy Dirac states and derive their space-time dynamics. Our analysis demonstrates that introducing orbital angular momentum provides a mechanism for amplifying the ZBW amplitude far beyond that of conventional Gaussian packets, while maintaining coherence. The resulting relativistic vortex states unify Gaussian and Bessel-Gaussian models within a single framework and opens new possibilities for observing relativistic quantum dynamics in structured electron wave packets.
Zitterbewegung (ZBW), arising from the interference between positive- and negative-energy solutions of the Dirac equation, is a characteristic feature of relativistic single-particle dynamics, but its explicit manifestation depends on the choice of position operator. We formulate relativistic vortex electron wave packets as coherent superpositions of Dirac plane-wave states and derive their exact spacetime evolution. For the canonical Dirac position, we show that orbital angular momentum substantially enhances and spatially structures the relative-coordinate contribution conventionally associated with ZBW. We then analyze the operator dependence of this result by separating the canonical position into a Foldy–Wouthuysen/Newton–Wigner (FW/NW) mean position and an oscillatory relative coordinate. For the vortex packets considered here, the FW/NW mean position exhibits only the ordinary centroid drift and no transverse trembling. However, the same vortex-enhanced radial scale survives in the positive-energy sector as a Berry-type geometric dressing of the projected position operator. The present work therefore identifies not a representation-independent trembling of the one-particle centroid, but a vortex-amplified remnant of Dirac interband mixing in an operationally meaningful position observable.
Six papers, one thesis: **Physics is adelic.** The Archimedean (real-number) description is the ∞\infty∞-place readout of a richer ultrametric structure defined over the p-adic completions of Q\mathbb{Q}Q. Ostrowski's theorem — which classifies all non-trivial completions of the rational numbers as R\mathbb{R}R and Qp\mathbb{Q}_pQp​ for each prime ppp — is the hidden organizing principle behind quantum measurement, quantum error correction, and the structure of spacetime at the Compton scale. We present the unified framework: Zitterbewegung (ZBW) is the physical manifestation of the p-adic channel of the adelic Dirac equation; Majorana zero modes are Bruhat-Tits fixed points encoding adelic topological charge; and adelic quantum error correction replaces active QEC codes with number-theoretic protection. This synthesis paper connects all six companion publications into a coherent research program with specific, falsifiable predictions. **Keywords:** Adelic physics, Ostrowski's theorem, Zitterbewegung, Bruhat-Tits tree, p-adic quantum mechanics, topological quantum computing, grand synthesis ---