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 $\mathcal{K}=\mathbf{A}\cdot \nabla$, with incompressible velocity field/vector potential $\mathbf{A}=\nabla \times \ddot{I}•=(-{\partial }_y,{\partial }_x)\ddot{I}•$. This operator has an infinitely degenerate subspace of zero energy eigenstates, arising from incompressibility, that are {\it extended} for generic $\ddot{I}•(\mathbf{x})$ and are expected to remain so under perturbation. I propose that an anomaly accounts qualitatively for properties of the spectrum and eigenstates of $\mathcal{K}$ and its perturbations.

Revised presentation; typographical errors corrected; no change in content