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Electron localisation, Lyapunov exponents and the symmetric group

The authors use the theory of the symmetric group to construct a generalised transfer matrix from which they can obtain the Lyapunov exponents of the original transfer matrix and the localisation lengths for an electron in a random potential. They compare their results with those of numerical simulations. The generalised transfer matrix has infinite dimensions but can in practice be truncated to finite dimensions. In the limit of an infinite matrix the theory is exact.