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Quantum mechanics is a strange business, and the quantum physics of strongly correlated many-electron systems can be stranger still. Good examples are the various quantum Hall effects. They are among the most remarkable many-body quantum phenomena discovered in the second half of the 20th century, comparable in intellectual import to superconductivity and superfluidity. The quantum Hall effects are an extremely rich set of phenomena with deep and truly fundamental theoretical implications.
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S. M. Girvin (2000) studied this question.
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