Possible long time tails in the current-current correlation function for the two dimensional electron gas in random magnetic field

TL;DR

This paper investigates the long-time behavior of current-current correlations in a two-dimensional electron gas subjected to a random magnetic field, revealing potential deviations from standard diffusive models.

Contribution

It identifies a class of diagrams leading to long time tails in the current-current correlation function, challenging the assumption of diffusive behavior in such systems.

Findings

Current-current correlation function exhibits logarithmic behavior at short times.

At longer times, the correlation decays as t^{-1}.

Results question the diffusive nature of electron dynamics in random magnetic fields.

Abstract

We consider two-dimensional degenerate electron gas in the presence of perpendicular random magnetic field. The magnetic field disorder which is assumed to be gaussian is characterized by two parameters. The first is proportional to the amplitude of local magnetic field fluctuations. The second one characterizes the disorder on the longer scale - we call it the screening length. Using Kubo formula for the conductivity we have found a class of diagrams which leads to the long time tails in the current - current correlation function. For short times comparing to the diffusion time corresponding to the screening length this function behaves like logarithm of time, for longer times it decays like $t^{-1}$ what of course puts in question the diffusive character of the behavior of the charged particle in random magnetic field widely assumed in the literature.