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

DOI: 10.5281/zenodo.21336123
Published: 2026-07-06

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

Rowan Quni — QNFO Research

Abstract

Zitterbewegung (ZBW), the relativistic trembling motion predicted by the Dirac equation, has eluded direct experimental observation in free electrons because its characteristic length scale is the Compton wavelength $\lambda_C \approx 2.4 \times 10^{-12}$ m. Guo, Xu & Gu (2025, arXiv:2511.21142) demonstrated that relativistic vortex electron wave packets carrying orbital angular momentum can amplify the ZBW amplitude far beyond the Gaussian-packet baseline. Predin (2026, arXiv:2604.08145) established an exact relation between ZBW dynamics and Berry curvature, identifying a time-independent observable. This paper assesses whether these advances enable ZBW detection in trapped-ion Dirac simulators, and connects the vortex mechanism to the p-adic observable framework of the Adelic Physics Program (Quni 2026, P1/P3/P7). [speculative]

1. The Zitterbewegung Gap

ZBW oscillates at $\omega{\mathrm{ZBW}} = 2mc^2/\hbar \approx 1.6 \times 10^{21}$ Hz with amplitude $\sim \lambdaC \approx 2.4 \times 10^{-12}$ m [established]. Trapped-ion Dirac simulators operate at $\sim 10^{-6}$ m resolution, requiring $\sim 10^{6}\times$ amplification.

2. Vortex-Enhanced ZBW

Guo et al. construct a relativistic vortex wave packet:

\[ \Psi_{\ell}(\mathbf{r}, t) = \int d^3 p \, e^{i\ell \phi_p} \, [c_+ u(\mathbf{p}) e^{-i E_p t/\hbar} + c_- v(\mathbf{p}) e^{+i E_p t/\hbar}] e^{i \mathbf{p}\cdot\mathbf{r}/\hbar} \]

Vortex OAM enhances ZBW amplitude "far beyond" Gaussian packets while maintaining coherence. The physical mechanism: the vortex singularity forces overlapping interference between positive- and negative-energy Dirac components.

3. Observable Framework

Predin (2026) defines the areal rate of Zitterbewegung: $\dot{\mathcal{A}}{\mathrm{ZBW}} = \frac{1}{2} \langle [\hat{x}, \hat{v}y] - [\hat{y}, \hat{v}_x] \rangle$. This observable is time-independent, determined by Berry curvature, and encodes chirality via its sign.

4. Connection to p-Adic Framework

The Adelic Physics Program formulates ZBW as a p-adic $\mathbb{Z}2$ topological invariant. Protocol C (Gromov $\delta$-hyperbolicity) compares Dirac vs. Majorana ZBW trajectories. Vortex amplification is synergistic with Protocol C if it preserves the $\mathbb{Z}2$ distinction.

5. Conclusion

The Guo et al. vortex mechanism, Predin areal-rate observable, and p-adic framework collectively point toward ZBW experimental feasibility. The key unknown is $\mathcal{A}(\ell)$, the amplification factor vs. topological charge. If $\mathcal{A}(\ell) \gtrsim 10^{6}$ for realizable OAM, ZBW becomes experimentally accessible for the first time.

Disconfirmed if $\mathcal{A}(\ell) \lesssim 10^{2}$ for any realizable $\ell$.

References

  1. Guo, Z., Xu, B. & Gu, Q. (2025). Vortex-Enhanced Zitterbewegung. arXiv:2511.21142v1.
  2. Predin, S. (2026). Chirality of ZBW and Berry curvature. arXiv:2604.08145v2.
  3. Quni, R. (2026). ZBW as a p-Adic Observable. doi:10.5281/zenodo.21214264.
  4. Quni, R. (2026). Bruhat-Tits Readout Protocol. doi:10.5281/zenodo.21214274.
  5. Quni, R. (2026). Adelic Physics Program. doi:10.5281/zenodo.21268809.