Quantum Interference Corrections in Electron Hydrodynamics

Abstract

We show that quantum-interference corrections in an electron fluid are tightly constrained by hydrodynamic Ward identities: charge and momentum conservation protect the $m=0,\pm1$ sectors, so the leading correction first appears in the spin-two $m=\pm2$ stress sector. The resulting hydrodynamic Cooperon has a robust infrared structure that renormalizes stress relaxation, and hence the viscosity. In channel flow this lowers the viscous resistivity, producing a hydrodynamic interference signature with the opposite sign to ordinary weak localization.