We derive a chiral kinetic theory with Landau level basis, which is valid for slow-varying magnetic field with arbitrary magnitude. We apply the new chiral kinetic theory to calculate the electric conductivity transverse to the magnetic field in a magnetized QED and QCD plasma. Under the lowest Landau level approximation and relaxation time approximation, we find the transverse conductivity approaches a constant in the large magnetic field limit and is inversely proportional to the relaxation time. We also obtain a frequency-dependent transverse conductivity in response to a time-dependent electric field. We find a high frequency enhancement in this conductivity.
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