Quantum-coherent transport in conductors whose linear dimensions are smaller than the phase-coherence length L_φ but larger than the elastic mean free path ℓ — i.e. the regime where the wave nature of electrons matters macroscopically yet…
mesoscopic-physics
Landauer-Büttiker formula: G = (2e²/h)·Σ T_n
Landauer 1957 / 1970 and Büttiker 1985-88 recast electrical conduction in the mesoscopic regime as a scattering problem: an elastic,…
Aharonov-Bohm effect: gauge-invariant phase, period Φ_0 = h/e
Aharonov-Bohm 1959 (Phys. Rev. 115:485) — a charged particle encircling a region of magnetic flux Φ acquires a gauge-invariant phase φ =…
Wiedemann-Franz law: κ/(σT) = π²k_B²/(3e²)
Wiedemann-Franz 1853 empirical law — for pure metals the ratio of thermal to electrical conductivity is proportional to temperature, with a…
Landauer: N open modes give G = N·G_0 exactly
Closed-form consequence of the Landauer-Büttiker formula at full transmission. For a ballistic, disorder-free conductor supporting N…
AB period Φ_0 = h/e, phase-per-period = 2π (exact)
Closed-form evaluation of the Aharonov-Bohm phase identity. Gauge-invariant phase φ(Φ) = (2π/Φ_0)·Φ with Φ_0 = h/e. Period: the phase…
Lorenz number L_0·e²/k_B² = π²/3 (exact rational π²)
Closed-form rational pin of the Sommerfeld Lorenz number. L_0 = π²·k_B²/(3·e²); rescaled ratio L_0·e²/k_B² = π²/3 exactly — a…