Non-fermi liquid as passive scalar fluid

Abstract

I suggest that electron localization by random flux and passive transport in quenched velocity fields in two dimensions be studied as perturbations of the simple operator ${\cal K}={\bf A} \cdot \nabla$, with incompressible velocity field/vector potential ${\bf A}=\nabla \times \phi=(-\partial_y,\partial_x)\phi$. This operator has an infinitely degenerate subspace of zero energy eigenstates, arising from incompressibility, that are {\it extended} for generic $\phi({\bf x})$ and are expected to remain so under perturbation. I propose that an anomaly accounts qualitatively for properties of the spectrum and eigenstates of ${\cal K}$ and its perturbations.