Quantum fluctuations in superconducting arrays with a general capacitance matrix

We study dissipation and quantum-fluctuation effects on the critical behavior of a superconducting array which has both self-capacitance and junction capacitance. The effective classical Hamiltonian is obtained through the use of the variational method in the path-integral formalism and then the renormalization-group technique is applied. A reentrant transition is found to exist for moderate quantum fluctuations; it persists regardless of the ratio of the junction capacitance to the self-capacitance although the junction capacitance tends to suppress the reduction of the transition temperature due to quantum fluctuations. As the strength of dissipation is increased, the reentrant behavior becomes weaker. The phase boundaries at zero temperature are obtained and compared with the results of the other mean-field approach. The system in the presence of an external magnetic field is also studied.