Phonon Boltzmann Transport Equation L1-497

Semiconductor PhysicsThermal phonon transportδ=5 · challengingL_DAG = 3.6📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

d n / d t + v_{g} . g r a d (n) = - (n - n_{B} E (T)) / t a u_{q, s}; k a pp a = q, s \sum C_{q, s} \cdot v_{g}, x^{2} \cdot t a u_{q, s}

BTE for phonon distribution n_{q,s}(r,t): drift with group velocity v_g + scattering (three-phonon, boundary, isotope); Callaway or full iterative treatment for thermal conductivity.

L-DAG

E.phonon_dispersion -> E.scattering_rates -> O.composite_method -> O.kappa

E.phonon_dispersionE.scattering_ratesO.composite_methodO.kappa

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 500

Well-posed; inversion for branch-resolved tau is ill-conditioned (only integrated kappa measured).

Solvability C

Solver class:: ShengBTE iterative solver; RTA approximation; ML-mediated dispersion fit
Convergence rate q:: 2
Complexity:: O(N_q^6 * N_branch)

Specs (0)

No L2 specs registered yet for this principle.