Alladi Ramakrishnan Hall

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

Nandan Pakhira

University of Queensland

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 ($\ll$ milli-$\Omega$-cm) 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 explore possible existence of such bounds in the incoherent regime of transport [4].


References :

1. A. Sommer, M. Ku, G. Roati, and M. W. Zwierlein, Nature 472, 201 (2011).

2. T. Enss, and R. Haussmann, Phys. Rev. Lett. 109, 195303 (2012).

3. Sean Hartnoll, Nat. Phys. 11, 54 (2014).

4. N. Pakhira and R. H. McKenzie, Phys. Rev. B 91, 075124 (2015).