## Thursday, July 17, 2014

### A quantum lower bound for the charge diffusion constant in strongly correlated metals?

Previously I posted about some interesting theory and cold atom experiments that suggest that the spin diffusion constant D has a lower bound of about hbar/m, where m is the particle mass.

Coincidentally, on the same day Sean Hartnoll posted a preprint, Theory of universal incoherent metallic transport. Based on results involving holographic duality [AdS/CFT] he conjectures that the diffusion constant satisfies the bound,

Dv2F/(kBT)

where v_F is the Fermi velocity.
I have pointed out to Sean that the ratio of this lower bound for D to the cold atom one (hbar/m) is
2 T_F/T where T_F is the Fermi temperature and T the temperature. Thus, the experiments [when normalised for trap effects] and the theory give a value of D about an order of magnitude smaller than Sean's lower bound. [My earlier post also references 2D cold atom experiments that give values for D several orders of magnitude smaller].
Sean raises the issue about how much m and T_F are renormalised by interactions. However, given that the spin susceptibility undergoes a small renormalisation it is not clear to me this will be significant.
Also, in a strongly interacting system charge and spin diffusion constants might be different.

In my post I pointed out the paucity of derivations of the central equation, the "Einstein relation", D=conductivity/susceptibility. However, Sean's preprint has a nice simple derivation of this based on conservation laws, but also showing how particle-hole asymmetry complicates things.