Linear-T resistivity vs Fermi liquid T² — the Planckian scattering rate ℏ/τ = αk_BT
Strange Metal ρ∝T
Fermi Liquid ρ∝T²
Phonon (Bloch) ρ∝T⁵
The Planckian scattering rate 1/τ = αk_BT/ℏ sets an apparent quantum limit on dissipation. Strange metals (cuprates, heavy fermions near QCP) show ρ = ρ₀ + AT with A ∝ k_B/(ℏe²v_Fk_F), violating the Fermi liquid prediction ρ ∝ T². The factor α ≈ 1 in optimally doped cuprates — remarkably close to the Planckian bound.