We analyse the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function technique is used to derive analytic results for the field-induced quantum mechanical drift motion of (i) single electrons and (ii) a dilute Fermi gas of electrons. The method yields the drift current and, at the same time it allows us to quantitatively establish the broadening of the (magnetic) Landau levels due to the electric field: level number k is split into k + 1 sublevels that render the kth oscillator eigenstate in energy space. Adjacent Landau levels will overlap if the electric field exceeds a critical strength. Our analysis suggests an alternative mechanism of conductivity quantization in the quantum Hall effect. The results are of particular relevance in strong current configurations where the presence of a perpendicular electric field must be taken into account.
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