Phonon Dispersion Relations L1-317

Quantum MechanicsLattice dynamicsδ=3 · standardL_DAG = 3.3📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

D_{ij, ab} (q) = n \sum P h i_{ij, ab} (R_{n}) e x p (- i q . R_{n}); d e t ∣ D - o m e g a^{2} \cdot I ∣ = 0

Harmonic phonon dispersion: dynamical matrix D_{ij}(q) from force constants Phi_{ij}; eigenvalues omega^2(q,s); thermal properties from sum over modes.

L-DAG

E.force_constants -> E.dynamical_matrix -> E.eigensolve -> O.phonon_dispersion

E.force_constantsE.dynamical_matrixE.eigensolveO.phonon_dispersion

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 200

Well-posed linear eigenproblem; inversion from INS is well-posed under symmetry constraints.

Solvability C

Solver class:: Quasi-harmonic approximation; frozen-phonon; DFPT (density functional perturbation)
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.