Numerical and analytical investigations of localisation in magnetic fields

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Abstract
Using a standard tight-binding model, the dependence of the localisation length xi on a perpendicular magnetic field in quasi-one-dimensional systems is investigated. A well known numerical method is used to calculate the localisation length as a function of the number of flux quanta per unit cell alpha and other system parameters. An attempt to explain the xi ( alpha ) curves perturbatively yields qualitative agreement and corrects the earlier results for xi as a function of energy and disorder W in the limit of large W obtained by similar techniques. Finally, the Lloyd model is re-examined with a magnetic field included. Previous claims of an exact solution for the Lloyd model for B=0 have been attacked but, the author believes not rigorously defeated. The author hopes to rehabilitate the Lloyd model by demonstrating its abilities in the magnetic field.

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