Hall effect and ballistic conduction in one-dimensional quantum wires

The nature of the Hall effect in one-dimensional ballistically conducting quantum channels is clarified by considering the current-induced transverse polarization of the channel, and by generalizing the concept of a Hall voltage to one dimension. The one-dimensional Hall effect can be observed noninvasively, is quantized, and is not quenched at low magnetic fields. A surprising conclusion is that the quantized resistance of narrow ballistic channels at $B=0\mathrm{}$ recently reported by Wharam et al. is a limiting case of the quantum Hall effect.