Are there quantum limits to diffusion in quantum many-body systems?Are there quantum limits to diffusion in quantum many-body systems?

Good metals like copper and gold show a high optical reflectivity (shiny), electrical and thermal conductivity. Good metals are characterised by diffusive transport of coherent quasi-particle states and the resistivity in these materials is well within the Mott-Ioffe-Regel (MIR) limit, $\frac{ha}{e^{2}}$ (where $a$ is the lattice constant). But in a wide range of strongly correlated materials and most notably in the strange metal regime of doped cuprates (high $T_{c}$ superconductor) the resistivity exceeds the MIR limit and the picture of coherent quasi-particle based transport breaks down. Recent cold atom experiments [1] and theory [2] of fermions near the unitary limit suggest a lower bound for the spin diffusion constant. Sean Hartnoll, loosely motivated by holographic duality (AdS/CFT correspondence) in string theory, proposed a lower bound to the charge diffusion constant $D \gtrsim \hbar v_{F}^{2}/(k_{B}T)$ in the incoherent regime of transport [3]. Using dynamical mean field theory (DMFT) we calculate the diffusion constant in the Hubbard model and find significant violation of Hartnoll's bound in the incoherent regime of transport [4].