-д хадгалсан:
| Үндсэн зохиолч: | |
|---|---|
| Формат: | Recurso digital |
| Хэл сонгох: | англи |
| Хэвлэсэн: |
Zenodo
2026
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| Нөхцлүүд: | |
| Онлайн хандалт: | https://doi.org/10.5281/zenodo.20097079 |
| Шошгууд: |
Шошго нэмэх
Шошго байхгүй, Энэхүү баримтыг шошголох эхний хүн болох!
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Агуулга:
- <p>The q-deformed Effective Field Theory (q-EFT) framework has demonstrated remark-<br>able predictive power in explaining galactic rotation curves without invoking dark matter<br>particles. A central feature across all applications is the empirical observation that the soli-<br>ton shape exponent n equals the topological winding number W. However, the theoretical<br>origin of this n= W relation—whether it emerges dynamically from quantum mechanics or<br>represents a contingent pattern—remained open.<br>This paper provides three independent theoretical lines of evidence that n = W is<br>dynamically selected by minimization of the quantum effective potential:<br>1. Local geometric consistency: Frobenius analysis shows n = W is the regular<br>solution at the soliton core, avoiding divergent energy density.<br>2. Quantum dynamical selection: Comprehensive numerical evaluation of the one-<br>loop effective potential for W = 1..20 demonstrates that the ground state locks to<br>n≈W with precision ∆n<0.023 across all topological sectors, with deviation scaling<br>as ∆n∝1/W1.1.<br>3. Robustness across topological sectors: The n = W relation persists uniformly<br>from low to high topological charge, suggesting a universal mechanism rather than an<br>accident of small-W dynamics.<br>These results establish n = W not as an ad hoc ansatz but as an emergent<br>property of the q-EFT quantum vacuum. The relation exhibits the characteristic signature<br>of a true quantum fixed point: logarithmic stability, energy ground state preference, and<br>scale-invariant deviation scaling.</p>