Anomalous Negative Magnetoresistance Caused by Non-Markovian Effects

A theory of recently discovered anomalous low-field magnetoresistance is developed for the system of two-dimensional electrons scattered by hard disks of radius $a,$ randomly distributed with concentration $n.$ For small magnetic fields the magentoresistance is found to be parabolic and inversely proportional to the gas parameter, $ \delta \rho_{xx}/\rho \sim - (\omega_c \tau)^2 / n a^2.$ With increasing field the magnetoresistance becomes linear $\delta \rho_{xx}/\rho \sim - \omega_c \tau $ in a good agreement with the experiment and numerical simulations.