Homogenization of hydrodynamic transport in Dirac fluids
Abstract
Large-scale electrical and thermal currents in ordinary metals are well approximated by effective medium theory: global transport properties are governed by the solution to homogenized coupled diffusion equations. In some metals, including the Dirac fluid of nearly charge neutral graphene, microscopic transport is not governed by diffusion, but by a more complicated set of linearized hydrodynamic equations, which form a system of degenerate elliptic equations coupled with the Stokes equation for fluid velocity. In sufficiently inhomogeneous media, these hydrodynamic equations reduce to homogenized diffusion equations. We recast the hydrodynamic transport equations as the infimum of a functional over conserved currents and present a functional framework to model and compute the homogenized diffusion tensor relating electrical and thermal currents to charge and temperature gradients. We generalize to this system to the well-known results in homogenization theory: Tartar’s proof of local convergence to the homogenized theory in periodic and highly oscillatory media and sub-additivity of the above functional in random media with highly oscillatory, stationary, and ergodic coefficients.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 2021
- Source ID
- 10.1063/5.0021961
Entities
People
- Andrew J. Lucas
- Guillaume Bal
- Mitchell Barry Luskin
Organizations
- Army Research Office
- National Science Foundation
- Office of Naval Research Global
- University of Chicago
- University of Colorado
- University of Minnesota