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Phys. Rev. B **37**, 3283–3294 (1988)
DOI:
10.1103/PhysRevB.37.3283

We have constructed a fully quantum-mechanical model of an ordered array of resistively shunted Josephson junctions, and have determined the nature of the phase diagram as a function of the Josephson coupling,*V*, the capacitance, *C* (or, equivalently, the charging energy *E*_{0}=4e^{2}/C), the shunt resistance, *R*, and the temperature, *T*. In order to treat the dissipative element (*R*) in a quantum system, we have modeled it by a heat bath with spectral weight chosen to reproduce Ohmic resistance in the classical limit. Among other results, we find that in the extreme quantum limit, *E*_{0}>>V>>k_{B}T, the onset of global phase coherence (superconductivity) in the array occurs only if *R* is less than a critical value *R*_{c}=Ah/e^{2}, where *A* is a number of order 1 which depends on the dimension and the lattice structure. The fact that the dissipation enters the thermodynamics at all is a consequence of the quantum nature of the transition. This transition is reminiscent of the results of recent experiments on thin films of granular superconductors.

We have constructed a fully quantum-mechanical model of an ordered array of resistively shunted Josephson junctions, and have determined the nature of the phase diagram as a function of the Josephson coupling,

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- 25.10.2009