By Günther Ludwig

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Kamimura and A. 76. S. M. Girvin and A. Brass, Phys. Rev. Lett. 63(1989) 2291; 2295. [54J L. P. C. Tsui and M. Shayegan, Surf. Sci. ZZ9(1990) 13. A. P. W. C. Tsui and M. Shayegan, Phys. Rev. Lett. 63(1989) 1731; G. Timp, R. E. Cunningham and R. E. Howard, Phys. Rev. Lett. 63(1989) 2268. K. A. Kivelson and N. Trivedi, Phys. Rev. Lett. 64(1990) 1297. W. Beenakker, Phys. Rev. Lett. H. MacDonald, Phys. Rev. Lett. 64(1990) 220. Scaling and the Quantum Hall Effect A. , London SW7 2BZ, UK An introduction to the ideas of scaling theory is given and the description of the quantum Hall effect in terms of a 2-parameter scaling theory is considered, mainly by studying the results of numerical simulations.

5(full squares) [491. heterostructures[44]. This is in conflict with the results obtained by Wakabayashi et al[45] for MOS inversion layers, which favour the finite-size scaling result[38]. To resolve the discrepancy, it seems that further numerical studies on the Landau-index dependence and the understanding of the temperature dependence of the electron-electron interaction effects are required. A most important problem in the physics of the quantum Hall effect is the following. Since delocalized states exist for H - 00, while all the states are localized for H=O, we can ask what happens when H is continuously decreased from 00 to 0, thereby increasing the mixing (overlap) of different Landau levels.

Int. Conf. Applications of High Magnetic Fields, Wiirzburg Springer Series in Solid State Sciences 87127 (1989) 4. Prange R E and Girvin S M: The Quantum Hall Effect (Graduate texts in Contemporary Physics) (Springer-Verlag, New York) (1987) 5. Chakraborty T and Pietilltinen P: The Fractional Quantum Hall Effect (Springer Series in Solid State Sciences 8S) (Springer-Verlag, Berlin Heidelberg) (1988) 6. Aoki H and Ando T: Solid State Commun: 38 1079 (1981) 7. LaughlinR B: Phys. Rev. B 235632 (1981) 8.