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For granular metallic films or two-dimensional arrays of Josephson junctions, fluctuations in the number of Cooper pairs are conjugate to the superconducting phase and can lead to zero-point destruction of phase coherence at zero temperature. In two dimensions the resulting critical behavior is shown to be that of the point of ^4He in three dimensions, with the charging energy playing the role of temperature. The nature of the quantum classical crossover and its effect on the frequency dependence of precursor diamagnetism near the quantum critical point are discussed.
Sebastian Doniach (Sun,) studied this question.