Non-Equilibrium Green's Function (NEGF) Quantum Transport L1-491

Semiconductor PhysicsNanoscale quantum transportδ=10 · hardL_DAG = 4📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

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Forward model E

G^{R} (E) = [E \cdot I - H - S i g m a^{R} (E)]^{- 1}; G^{<} = G^{R} \cdot S i g m a^{<} \cdot G^{A}; I = (2 e / h) \cdot in t e g r a l T r [S i g m a_{L}^{<} \cdot G^{R} \cdot G amm a_{R} \cdot G^{A} - G amm a_{L} \cdot G^{<} ...] d E

Keldysh-Kadanoff-Baym NEGF: retarded G^R, advanced G^A, lesser G^< Green's functions; self-energies Sigma^R, Sigma^< for contacts and scattering; Landauer current.

L-DAG

E.hamiltonian_build -> E.self_energy -> E.eigensolve -> O.current_LDOS

E.hamiltonian_buildE.self_energyE.eigensolveO.current_LDOS

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 5000

Dyson equation is numerically well-posed in principle but conditioning deteriorates with device size; self-consistent Born (SCBA) loops add non-linear coupling.

Solvability C

Solver class:: Recursive Green's Function (RGF); contact block reduction (CBR); adjoint-NEGF for inversion
Convergence rate q:: 2
Complexity:: O(N_orbital^3 * N_energy)

Specs (0)

No L2 specs registered yet for this principle.