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Non-universal tunneling resistance at the quantum critical point of mesoscopic SQUIDs array

We calculate the tunnelling resistance at the quantum critical point of a mesoscopic SQUIDs array in the presence of magnetic flux. We find the analytical relation between the magnetic flux induced dissipation strength and the Luttinger liquid parameter of the system. While the experimental finding for the system is around 40-50 mK, we find the behavior of the system even at lower temperatures through the analysis of renormalization group. Apart from the length scale dependent superconductor-insulator transition, we also predict the evidence of length scale independent metallic state. This study also emphasizes the importance of Co-tunelling effect.