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| Format: | Recurso digital |
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Zenodo
2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.19020167 |
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| _version_ | 1866901063001440256 |
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| author | 王有福 |
| author_facet | 王有福 |
| contents | <p> </p> <p>This work proposes a unified low-mode field framework describing critical mode mixing, slow-mode formation, and family structure generation across different physical systems.</p> <p> </p> <p>The theory is formulated using a mother field defined on an extended manifold with an internal compact geometry. Through eigenmode decomposition and low-mode truncation, the dynamics reduce to an effective two-mode interaction structure characterized by parameters (A,B,C,Γ). These parameters can be compressed into dimensionless variables (δ,c,γ), forming a universal kernel that governs mixing strength, spectral splitting, mixing angle, and critical slowdown.</p> <p> </p> <p>The framework predicts a universal stability condition</p> <p> </p> <p>δ² + c² < 1</p> <p> </p> <p>with the boundary δ² + c² = 1 corresponding to slow-mode formation. Numerical scans reveal a universal phase diagram describing weak mixing, hybridization, and slow-mode regions.</p> <p> </p> <p>The theory also provides a structural explanation for the emergence of three family states through internal eigenmode windows. The framework applies to multiple physical systems including photonic crystals, phonon dispersions, magnon hybridization, and quantum level mixing.</p> <p> </p> <p>This work provides a unified structural language for critical mode mixing phenomena and suggests a cross-system theoretical framework for studying critical dynamics.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19020167 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | A Unified Low-Mode Field Framework for Critical Mode Mixing and Family Structure 王有福 <p> </p> <p>This work proposes a unified low-mode field framework describing critical mode mixing, slow-mode formation, and family structure generation across different physical systems.</p> <p> </p> <p>The theory is formulated using a mother field defined on an extended manifold with an internal compact geometry. Through eigenmode decomposition and low-mode truncation, the dynamics reduce to an effective two-mode interaction structure characterized by parameters (A,B,C,Γ). These parameters can be compressed into dimensionless variables (δ,c,γ), forming a universal kernel that governs mixing strength, spectral splitting, mixing angle, and critical slowdown.</p> <p> </p> <p>The framework predicts a universal stability condition</p> <p> </p> <p>δ² + c² < 1</p> <p> </p> <p>with the boundary δ² + c² = 1 corresponding to slow-mode formation. Numerical scans reveal a universal phase diagram describing weak mixing, hybridization, and slow-mode regions.</p> <p> </p> <p>The theory also provides a structural explanation for the emergence of three family states through internal eigenmode windows. The framework applies to multiple physical systems including photonic crystals, phonon dispersions, magnon hybridization, and quantum level mixing.</p> <p> </p> <p>This work provides a unified structural language for critical mode mixing phenomena and suggests a cross-system theoretical framework for studying critical dynamics.</p> |
| title | A Unified Low-Mode Field Framework for Critical Mode Mixing and Family Structure |
| url | https://doi.org/10.5281/zenodo.19020167 |