Thursday, June 4, 2015

Violation of quantum bounds on the viscosity of strongly interacting fermion fluids

Nandan Pakhira and I just finished a paper
Shear viscosity of strongly interacting fermionic quantum fluids

Eighty years ago Eyring proposed that the shear viscosity of a liquid, η, has a quantum limit η larger than n hbar where n is the density of the fluid. Using holographic duality and the AdS/CFT correspondence in string theory Kovtun, Son, and Starinets (KSS) conjectured a universal bound η/s ≥ hbar/4πk_B for the ratio between the shear viscosity and the entropy density, s.

Using Dynamical Mean-Field Theory (DMFT) we calculate the shear viscosity and entropy density for an fermion fluid described by a single band Hubbard model at half filling. Our calculated shear viscosity as a function of temperature is compared with experimental data for liquid 3He. At low temperature the shear viscosity is found to be well above the quantum limit and is proportional to the characteristic Fermi liquid 1/T^2 dependence, where T is the temperature. With increasing temperature and interaction strength U there is significant deviation from the Fermi liquid form.

Also, the shear viscosity violates the quantum limit near the crossover from coherent quasi-particle based transport to incoherent transport (the bad metal regime). Finally, the ratio of the shear viscosity to the entropy density is found to be comparable to the KSS bound for parameters appropriate to liquid 3He. However, this bound is found to be strongly violated in the bad metal regime for parameters appropriate to lattice electronic systems such as organic charge transfer salts.

We welcome any comments.


  1. But you already know that in a theory of transport without vertex corrections that the transport lifetime is proportional to the single particle lifetime and that the latter can be arbitrarily small for a bad metal. What about using a conserving theory of transport?

  2. Dear Edward,

    Thanks for your comment.
    Your question is excellent. Including the vertex corrections is very challenging and certainly worth pursuing. We did not do this since in DMFT they are not included. Other calculations, in different contexts (for example by Tremblay and collaborators) find that vertex corrections change things by of order one. In contrast, some of the violations of the conjectured quantum limits are by several orders of magnitude and so I would be confident are results are robust in that regard.

    These issues are discussed somewhat at the end of our first paper.

    Readers who want some background on vertex corrections my find this old post helpful