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E_y = \omega_\textrm{c} \tau E_x \\  j_x = \sigma_0 E_x  \end{equation}  This effect is just the classical Hall effect: the conductance in the $x$ direction remains unchanged, with the magnetic field creating an electric field in the $y$ direction due to redistribution of charge. However, this derivation hinges on a crucial assumption: \emph{all} charge carriers have the same decay time. We've seen that not to be true in the case of the Landau quasiparticles -- their decay time depends on how far away their energy is to the Fermi energy.     Therefore, in a Fermi Liquid,