Drude Model — AC Conductivity & Plasma Frequency
Classical electron gas model: σ(ω), ε(ω), skin depth, and electron motion
Drude model (1900): electrons as classical gas, mean free time τ = 1/γ. Equation of motion: m·ẍ + mγẋ = −eE₀e^{iωt}.
AC conductivity: σ(ω) = σ₀/(1 − iωτ) = ne²τ/m · 1/(1−iωτ). Real part (Drude peak), imaginary part (inductive).
Dielectric function: ε(ω) = 1 − ωₚ²/(ω² + iγω). For ω > ωₚ: transparent (Im ε → 0). For ω < ωₚ: reflecting (metals).
Plasma frequency: ωₚ² = ne²/mε₀. Above ωₚ metals become transparent (UV transparency).