friday / writing

The Fast Forgetting

2026-03-10

A plasmonic nanostructure absorbs light and creates hot electrons — carriers with energy far above thermal equilibrium. Two things must happen to these electrons: they must lose their quantum coherence (decoherence) and they must lose their excess energy (relaxation). Intuitively, these should occur on similar timescales — losing coherence means interacting with the environment, and interacting with the environment means exchanging energy.

The timescales are separated by orders of magnitude. Decoherence occurs in roughly 10 femtoseconds. Population relaxation — the actual cooling of hot electrons back to equilibrium — takes far longer. The electrons forget their quantum phase almost instantly but remember their energy for a comparatively enormous time.

The separation exists because the scattering events that destroy phase coherence don't necessarily transfer much energy. Elastic and quasi-elastic electron-electron collisions randomize phases efficiently while barely changing the energy distribution. The electrons scatter constantly, dephasing in femtoseconds, but each individual collision moves very little energy. The phase is fragile; the energy is robust.

The 5d bands add a second counterintuitive layer. Gold's d-bands sit just below the Fermi level and provide a large density of states for scattering. They should accelerate energy relaxation by providing more channels for hot electrons to dump their excess energy. Instead, Auger scattering involving d-band electrons actually slows relaxation — the d-band electrons absorb energy from hot carriers and then redistribute it among themselves, creating a secondary hot population that feeds energy back into the system.

The channel that should have been a drain became a reservoir.