Is there a quantum limit to diffusion in quantum many-body systems?

Nandan Pakhira and I recent completed a paper
Absence of a quantum limit to charge diffusion in bad metals

This work was partly motivated by

- a recent proposal, using results from the AdS-CFT correspondence, by Sean Hartnoll that there was a quantum limit to the charge diffusion constant in bad metals,

- experimental observation and theoretical calculations of a limit to the spin diffusion constant in cold atom fermions near the unitarity limit.

We calculated the temperature dependence of the charge diffusion constant in the metallic phase of a Hubbard model using Dynamical Mean-Field Theory (DMFT).

The figure below shows  the temperature dependence of the charge diffusion constant for a range of values of the Hubbard U. The temperature and energy scale is the half-bandwidth W. The Mott insulator occurs for U larger than about 3.4 W.

Violations of Hartnoll's bound occurs in the same incoherent regime as violations of the Mott-Ioffe-Regel limit on the resistivity.

We also find that the charge diffusion constant can have values orders of magnitude smaller than the cold atom bound on the spin diffusion constant.

We welcome discussion and comments.