Hamiltonian renormalization, Fermi liquid theory and hydrodynamic transport in ultracold Fermi gases
Hadrien Kurkjian (LPTMC, Paris)
I will derive the Navier-Stokes equations that describe the hydrodynamic behavior of a gas of spin-1/2 fermions at low temperatures. The difficult part of the derivation is to obtain accurate expressions of the transport coefficients (viscosity, thermal conductivity and spin diffusivity) that control the dissipative terms of the Navier-Stokes system. For this, I will introduce a low-energy effective theory that extends Fermi liquid theory to account for the quasiparticle collision amplitudes in all directions. This results in an exact expansion of the transport coefficients in power of the s-wave scattering length a, which one can view as the equivalent for transport of the Lee-Huang-Yang expansion of the equation of state. I will confront our results to existing measurements of the viscosity and spin diffusivity of ultracold Fermi gases. If time permits, I will also discuss how our effective theory applies to the superfluid phase, and in particular to two-fluid hydrodynamics.