 Hamiltonian ray equations for a local dispersion relation

ID: hamiltonian-ray-equations-for-a-local-dispersion-relation

Codex  0 Created 2026-10-06 Updated 2026-10-14

ω = Ω (k; X, T)

yields

\frac{d X}{d T} = \nabla_{k} Ω, \frac{d k}{d T} = - \nabla_{X} Ω_{k}, \frac{d ω}{d T} = Ω_{T}_{k} .

The spatial and temporal derivatives on the right hold the wavevector fixed. Translation symmetries conserve the corresponding wavevector components, while time independence conserves frequency.

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