EQUATION REGISTRY

Intersection of moving-source and radiation spectra

Isotropic gapped branch, v<c. ωs<ω₀/γ has no intersection; equality is critical tangency, not strictly subthreshold. Outgoing flux also requires source projection.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 5

ASD-WEB-QM-007
ωa(k)=k⋅v+ωs,min⁡k[ω02+c2k2−k⋅v]=ω0/γ\omega_a(\mathbf k)=\mathbf k\cdot\mathbf v+\omega_s,\qquad\min_{\mathbf k}\left[\sqrt{\omega_0^2+c^2k^2}-\mathbf k\cdot\mathbf v\right]=\omega_0/\gamma

Isotropic gapped branch, v<c. ωs<ω₀/γ has no intersection; equality is critical tangency, not strictly subthreshold. Outgoing flux also requires source projection.
Chapter reference: Ch. 5 (5.1.28)–(5.1.29) · ASD-BOOK-ddbade997b45

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Adopted source, conditions and previous versions

Ch. 5 (5.1.28)–(5.1.29)

Isotropic gapped branch, v<c. ωs<ω₀/γ has no intersection; equality is critical tangency, not strictly subthreshold. Outgoing flux also requires source projection.

Conditions retained in this adoption

  • Selected channel and stated initial/boundary conditions; action/energy matching retained
  • Continuum, slow-envelope and detector approximations kept at their respective levels

Specific unresolved source issues

  • QC-THRESHOLD-001: strict versus non-strict radiation threshold

Source locators: p1792 · p1809 · p1822 · p1823 · p1846 · p1857

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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QM-0accdcbe7725 · Ch. 5 (5.1.28)–(5.1.29)

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