Minimal Theory of Strange Carriers

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 $D=\hbar/m$, 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 $\lambda_{dB}$ 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 wavefunction.