I explore a theory of transport and optical properties of strange metallic carriers in strongly correlated systems that follows from assuming that the diffusion constant has reached its quantum limit $D=\hslash /m$, and that such quantum carriers behave as distinguishable particles as they would in an electronic solid. These assumptions immediately lead to $T$-linear resistivities with apparent Planckian scattering rates and, extending to the frequency domain, to the stretched Drude peaks and $\omega /T$ scaling commonly observed in optical absorption experiments in strange metals. This behavior can be rationalized by observing that when the thermal de Broglie length ${\lambda }_{\mathrm{dB}}$ exceeds the mean-free path, the carrier motion can no longer be described in terms of random collisions of classical particles as assumed by Drude-Boltzmann theory and should be viewed instead as a sequence of projective measurements collapsing the wave function.

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• Carrier dynamics
• Electrical conductivity
• Electron relaxation
• Optical conductivity
• Transport phenomena
• High-temperature superconductors
• Strongly correlated systems