In a small sample the fractional QH

In a small sample the fractional QHE can occur in the absence of disorder and can show deviations from precise quantization. Moreover, in special geometries481 GH can take on quantized values that are not simply related to e∗. These observations cannot be easily understood within the conventional description of the fractional QHE, as outlined in the previous subsection. An approach along the lines of the edge channel formulation of the integer QHE (Sections IV.A and IV.B) seems more promising. In Ref.482 the concept of an edge channel was generalized to the fractional QHE, and a generalized Landauer formula relating the conductance to the transmission probabilities of the edge channels was derived. We review this theory and the application to experiments. A different edge channel theory by MacDonald483 is discussed toward the end of this subsection.