Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1998-11-25
Physics
High Energy Physics
High Energy Physics - Theory
Talk presented at the Workshop on the Exact Renormalisation Group, Faro, Portugal, 10-12th September, 1998. Typeset in Latex,
Scientific paper
An analytic form for the crossover of the conductivity tensor between two Hall plateaux, as a function of the external magnetic field, is proposed. The form of the crossover is obtained from the action of a symmetry group, a particular subgroup of the modular group, on the upper-half complex conductivity plane, by assuming that the beta-function describing the crossover is a holomorphic function of the conductivity. The group action also leads to a selection rule, |p_1q_2-p_2q_1|=1, for allowed transitions between Hall plateaux with filling factors p_1/q_1 and p_2/q_2, where q_1 and q_2 are odd.
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