A previously unnoticed group structure for the transfer matrices of mesoscopic systems is identified. From the invariant measure for this group and a maximum entropy ansatz we derive the Laguerre ensemble of random matrices. A comparison with the Hofstadter model shows that the Laguerre ensemble provides a quantitative description of scattering in mesoscopic systems under applied magnetic fields.
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Slevin et al. (1993) studied this question.
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