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We consider quantum fluctuations of current in a metallic loop induced by varying magnetic flux. The dependence of the fluctuations on the flux change Φ contains a logarithmically divergent term periodic in Φ with the period Φ₀=hc/e. The fluctuation is smallest near Φ=nΦ₀. The divergence is explained by a comparison with the orthogonality catastrophe problem. The Φ₀-periodicity is related with the discreteness of "attempts" in the binomial statistics picture of charge fluctuations.
Lee et al. (1993) studied this question.