Scaling, Diffusion, and the Integer Quantized Hall Effect

Abstract

The behavior of the two-particle spectral function, $S(q,\omega )$, is examined in the hydrodynamic regime, at the mobility edge in a model for the integer quantized Hall effect. Results are presented from numerical diagonalization of the Hamiltonian for finite systems. For $\frac{q^2}{\omega }$ small, $S(q,\omega )$ has a conventional, diffusive form. For $\frac{q^2}{\omega }$ large, the novel dependence $S(q,\omega )\sim {\omega }^{-\frac{\eta }{2}}{q}^{-2+\eta }$ is obtained, with $\eta =0.38\mathrm{}\pm 0.04$.