Passive Scalars, Random Flux, and Chiral Phase Fluids

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 analytical techniques we argue that both systems have extended eigenstates at a special point in the spectrum invariant under particle-hole symmetry, 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.