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The behavior of non interacting electrons is studied in two-dimensional disordered systems under a perpendicular magnetic field. The strong-field limit is examined, in which scattering between Landau bands may be neglected. It is shown that the form of the two-particle spectral function is severely restricted by a general inequality for certain eigenfunction correlations, together with the requirements of average translational and rotational invariance. Consequences are: there cannot exist bands of extended states (in the diffusion sense) with finite energy width; and either the exponent nu O (which would be new in two-dimensional localisation).
J. T. Chalker (1987) studied this question.