Dynamical Selection of Soliton Profiles in q-Deformed Effective Field Theory: Quantum n = W Locking with Complete Numerical Verification
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| Format: | Recurso digital |
| Language: | English |
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2026
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| _version_ | 1866901608009302016 |
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| author | Wei, Da |
| author_facet | Wei, Da |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20097079 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Dynamical Selection of Soliton Profiles in q-Deformed Effective Field Theory: Quantum n = W Locking with Complete Numerical Verification Wei, Da $q$-deformed Effective Field Theory ($q$-EFT) Topological Solitons Spontaneous Symmetry Breaking Quantum $n=W$ Locking One-loop Effective Potential Quantum Chiral Anomaly Galactic Rotation Curves Dark Matter Alternative <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> |
| title | Dynamical Selection of Soliton Profiles in q-Deformed Effective Field Theory: Quantum n = W Locking with Complete Numerical Verification |
| topic | $q$-deformed Effective Field Theory ($q$-EFT) Topological Solitons Spontaneous Symmetry Breaking Quantum $n=W$ Locking One-loop Effective Potential Quantum Chiral Anomaly Galactic Rotation Curves Dark Matter Alternative |
| url | https://doi.org/10.5281/zenodo.20097079 |