Theoretical Research in Statistical Mechanics

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Theoretical research will be conducted on various aspects of systems which have topological quantum numbers. Research on the quantum Hall effect will be continued and the question of where the current is generated in a Hall device should be clarified. Work on the analogy between the quantum Hall effect in a two-dimensionally modulated system and the theory of phase transitions will also be continued. New work on the motion of quantized vortices in superfluid helium at very low temperatures is being started. A comprehensive review of topological quantum numbers will be written. %%% Theoretical research will be conducted on the meaning and cause of various quantum effects. Systems to be investigated include the two-dimensional electron gas and its manifestation through the quantum Hall effect and superfluid helium. The influence of various defect structures, such as vortices, will be the focus of this work.