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By Ruark A.E.

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H (12) The quantity h/eB has the dimension of an area and we shall have more to say about it. The fact that Planck’s constant appears explicitly in this expression suggests that quantum mechanics plays a crucial role in the formation of those plateaus in ρxy . But before analyzing the new features induced by quantum mechanics, it is useful to first describe in more detail the Hamiltonian approach to classical motion. 3 Hamiltonian formalism Let us introduce a vector potential A(r) for the magnetic field: B = ∂x Ay − ∂y Ax .

In addition they can be simultaneously realized in laboratories all over the world which strongly simplifies and improves the traceability of any measurements to the primary standards. With the discovery of the Josephson and the quantum Hall effects, two electrical quantum standards became available. As a first consequence, the worldwide consistency in the realization and maintenance of the electrical units and the electrical measurements based on them has improved hundredfold in the last decade. The two quantum effects will certainly also play a major role in the next modernization of the SI when the last remaining base unit in the SI still based on an artefact, the kilogram, will be linked to fundamental constants.

Physics in a Strong Magnetic Field 31 Imagine now that we continuously fill a bounded region of the plane with noninteracting electrons. Let n be the electron number density. We introduce the so called filling factor as the number of electrons per cell: ν = n2πl2 . (31) Due to the Pauli principle, a cell can be occupied by one electron only per energy level. Therefore, each time the filling factor reaches an integer, an energy level gets filled and the next electron must be added to the next energy level.

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