[en] The authors study collisionless conductivity produced by chaotic scattering and stochastic diffusion of particles in the current sheet. They look at the effect of a constant cross tail magnetic field B_y in the case of a parabolic geometry. They show that the correlation time scales as (B_y/B_z)², and infer that linear tearing modes should be stabilized with increasing values of B_y. This tendency toward stabilization seems to be stronger when one introduces electrons into the calculations. The authors have derived the collisionless conductivity in terms of an ensemble averaged power spectrum of the single particle trajectories. This approach toward solution of the problem allows for direct calculation of the linear conductivity. In addition the use of the power spectrum gives direct evidence of the chaotic particle dynamics in the general problem of collisionless irreversible resistivity