By Rudolf F. Geyer, Johannes van der Zouwen
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Extra resources for Sociocybernetics: Complexity, Autopoiesis, and Observation of Social Systems (Controversies in Science)
Sample text
In this case, it is no longer possible to preserve such a simple description of quantum energy eigenstates. Nevertheless, as shown on Fig. 3 illustrating the effect of a strong scatterer modeled as an impenetrable disk of radius a, even when a is small compared to the cyclotron radius, we may expect that such a scatterer does not disturb the shape of a strip-like eigenstate excepted in its immediate vicinity. In particular, the overall direction of propagation of a wave-packet is not modified by the presence of such impurities.
In this article, mainly the aspects of the QHE relevant for its metrological application are reviewed. After a short introduction of the theoretical models describing the integer QHE, the properties of the devices used in metrology and the measurement techniques are described. A detailed summary is given on the measurements carried out to demonstrate the universality of the quantized Hall resistance and to assess all the effects leading to deviations of the Hall resistance from the quantized value.
We obtain: e2 e2 (W (x0 , Ly ) − W (x0 , 0)) = (V (Ly ) − V (0)) . (54) h h Again, this result is independent of the strength of the impurity potential. Such a 2 fully occupied level provides therefore a contribution equal to eh to the total Hall conductance. Ix,n (x0 ) = Physics in a Strong Magnetic Field 37 3)En (x0 , 0) > µ and En (x0 , Ly ) < µ. Then e2 µ − En (x0 , Ly ) . h e Ix,n (x0 ) = (55) 4)En (x0 , 0) < µ and En (x0 , Ly ) > µ. Then Ix,n (x0 ) = e2 En (x0 , 0) − µ . h e (56) These last two cases correspond to Landau levels which are partially filled in the absence of impurity potential, but in the presence of the driving field.