We study the conductance of chaotic or disordered wires in a situation where equilibrium transport decomposes into biased diffusion and a counter-moving regular current. A possible realization is a semiconductor nanostructure with transversal magnetic field and suitably patterned surfaces. We find a non-trivial dependence of the conductance on the wire length which differs qualitatively from Ohms law by the existence of a characteristic length scale and a finite saturation value.
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