Collective Modes and Topological Excitations in Layered Vector Phase Systems (Paper II in the Layered Phase Series)
Fuente:
Zenodo
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866901781487812608 |
|---|---|
| author | Sano, Ryosuke |
| author_facet | Sano, Ryosuke |
| contents | <p>Abstract</p> <p>We extend the minimal layered phase framework of Paper I [1] in two steps.</p> <p>First, we introduce the minimal inter-layer synchronisation potential consistent with</p> <p>the global U(1) symmetry of the scalar model. Spontaneous symmetry breaking</p> <p>produces a massless Goldstone mode and N−1 massive relative modes. Canonical</p> <p>normalisation of the Goldstone mode yields the exact coupling suppression geff =</p> <p>gN−1/2, with no adjustable parameters.</p> <p>In the second step, we replace the scalar target space S1 with the vector target</p> <p>space S2, the minimal extension that admits a non-trivial Hopf invariant QH ∈Z.</p> <p>We show that integrating out the massive relative modes generates a Skyrme–</p> <p>Faddeev quartic term in the effective Lagrangian, which evades Derrick’s theorem</p> <p>and stabilises three-dimensional solitons (Hopfions). The Vakulenko–Faddeev en-</p> <p>ergy bound E ≥C(Nf2)1/2κ1/2|QH|3/4 then implies a discrete, topologically pro-</p> <p>tected excitation spectrum. A variational estimate gives Emin(2)/Emin(1) ≈1.63.</p> <p>All results follow from the microscopic Lagrangian and established mathematical</p> <p>theorems without fine-tuning. Exchange statistics of Hopfions are addressed in Pa-</p> <p>per III</p> <p> </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19571171 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Collective Modes and Topological Excitations in Layered Vector Phase Systems (Paper II in the Layered Phase Series) Sano, Ryosuke Goldstone Mode <p>Abstract</p> <p>We extend the minimal layered phase framework of Paper I [1] in two steps.</p> <p>First, we introduce the minimal inter-layer synchronisation potential consistent with</p> <p>the global U(1) symmetry of the scalar model. Spontaneous symmetry breaking</p> <p>produces a massless Goldstone mode and N−1 massive relative modes. Canonical</p> <p>normalisation of the Goldstone mode yields the exact coupling suppression geff =</p> <p>gN−1/2, with no adjustable parameters.</p> <p>In the second step, we replace the scalar target space S1 with the vector target</p> <p>space S2, the minimal extension that admits a non-trivial Hopf invariant QH ∈Z.</p> <p>We show that integrating out the massive relative modes generates a Skyrme–</p> <p>Faddeev quartic term in the effective Lagrangian, which evades Derrick’s theorem</p> <p>and stabilises three-dimensional solitons (Hopfions). The Vakulenko–Faddeev en-</p> <p>ergy bound E ≥C(Nf2)1/2κ1/2|QH|3/4 then implies a discrete, topologically pro-</p> <p>tected excitation spectrum. A variational estimate gives Emin(2)/Emin(1) ≈1.63.</p> <p>All results follow from the microscopic Lagrangian and established mathematical</p> <p>theorems without fine-tuning. Exchange statistics of Hopfions are addressed in Pa-</p> <p>per III</p> <p> </p> |
| title | Collective Modes and Topological Excitations in Layered Vector Phase Systems (Paper II in the Layered Phase Series) |
| topic | Goldstone Mode |
| url | https://doi.org/10.5281/zenodo.19571171 |