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The integer quantum Hall transition and random su(N) rotation

We reduce the problem of the integer quantum Hall transition (QHT) to a random rotation of an N-dimensional vector by using an su(N) algebra, where only N specially selected generators of the algebra are nonzero. The group-theoretical structure revealed in this way allows us to obtain a new series of conservation laws for the equation describing the electron density evolution in the lowest Landau level. The resulting formalism is particularly well suited to numerical simulations, allowing us to obtain the critical exponent ν numerically in a very simple way. We also suggest that if the number of nonzero generators is much less than N, the same model, in a certain intermediate time interval, describes percolating properties of a random incompressible steady two-dimensional flow. In other words, the QHT in a very smooth random potential inherits certain properties of percolation.