Higher derivative corrections to incoherent metallic transport in holography

Transport in strongly-disordered, metallic systems is governed by diffusive processes. Based on quantum mechanics, it has been conjectured that these diffusivities obey a lower bound D/upsilon(2) greater than or similar to h/k(B)T, the saturation of which provides a mechanism for the T-linear resistivity of bad metals. This bound features a characteristic velocity upsilon, which was later argued to be the butterfly velocity upsilon B, based on holographic models of transport. This establishes a link between incoherent metallic transport, quantum chaos and Planckian timescales. Here we study higher derivative corrections to an effective holographic action of homogeneous disorder. The higher derivative terms involve only the charge and translation symmetry breaking sector. We show that they have a strong impact on the bound on charge diffusion D-c/upsilon(2)(B) greater than or similar to h/k(B)T, by potentially making the coefficient of its right-hand side arbitrarily small. On the other hand, the bound on energy diffusion is not affected.