Length-Scale Dependent Superconductor-Insulator Quantum Phase Transition in One Dimension

We study the dissipation physics of one dimensional mesoscopic superconducting quantum interference device array by using the field-theoretical renormalization group method. We observe length scale dependent superconductor-insulator quantum phase transition at very low temperature and also observe the dual behaviour of the system for the higher and lower values of magnetic field. At a critical magnetic field, we also observe a critical behaviour where the resistance is independent of length.