Passive scalars, random flux, and chiral phase fluids

TL;DR

This paper investigates localization phenomena in two-dimensional classical and quantum particles influenced by quenched random fields, revealing extended states at a critical energy point and conformal invariance features.

Contribution

It introduces a combined numerical and analytic approach to identify extended eigenstates and conformal invariance in 2D localization with random flux and vorticity fields.

Findings

Extended eigenstates at a special spectrum point $E_c$

Conformal invariance ratios in Lyapunov exponents

Determination of eigenstate decay behavior

Abstract

We study the two-dimensional localization problem for (i) a classical diffusing particle advected by a quenched random mean-zero vorticity field, and (ii) a quantum particle in a quenched random mean-zero magnetic field. Through a combination of numerical and analytic techniques we argue that both systems have extended eigenstates at a special point in the spectrum, $E_c$, where a sublattice decomposition obtains. In a neighborhood of this point, the Lyapunov exponents of the transfer-matrices acquire ratios characteristic of conformal invariance allowing an indirect determination of $1/r$ for the typical spatial decay of eigenstates.