Drude

Paul Karl Ludwig Drude (1863–1906) was a German physicist who formulated the classical free-electron model of electrical conduction in metals, now known as the Drude model. The model treats conduction electrons as a gas of classical charges that move freely between random, instantaneous collisions.

Drude studied at the University of Göttingen and published Zur Elektronentheorie der Metalle in 1900, outlining the theoretical framework for electron transport in metals. The model yields a simple expression for DC conductivity and provides a qualitative account of metallic behavior, linking macroscopic transport to microscopic collision processes.

The Drude model describes the DC conductivity by σ = n e^2 τ / m, where n is electron density, e the electron charge, m the electron mass, and τ the average time between collisions (the relaxation time). It also leads to a frequency-dependent dielectric response, ε(ω) ≈ ε∞ − ω_p^2 /(ω^2 + iω/τ), with the plasma frequency ω_p^2 = n e^2 /(ε0 m). This framework captures the plasma-like response of metals at optical frequencies and helps explain reflectivity and screening in the low-frequency regime.

Extensions and legacy: The Drude model was refined by Lorentz (Drude-Lorentz model) to include bound electrons, and by Sommerfeld to incorporate quantum statistics, forming the Drude-Sommerfeld theory. While its classical nature limits quantitative accuracy, the model remains a foundational pedagogical tool and a milestone in the development of modern band theory and quantum transport.