Non-fermi liquid as passive scalar fluid

TL;DR

This paper explores the spectral properties of a passive scalar fluid model in two dimensions, focusing on electron localization and the effects of perturbations on the operator governing passive transport.

Contribution

It introduces a novel perspective on passive scalar transport as a perturbation of a degenerate operator with incompressible velocity fields, highlighting the role of anomalies in spectral properties.

Findings

Extended zero energy eigenstates due to incompressibility.

Anomalies qualitatively explain spectral and eigenstate properties.

Perturbations preserve the extended nature of eigenstates.

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.