Phase transition in superconducting arrays with external currents

Abstract
A two-dimensional superconducting array with applied external currents is studied in an analytical way. We obtain a Fokker-Planck equation from the Langevin equation ruling the time evolution of the system, and introduce a pseudo-Hamiltonian to describe the stationary solution of the Fokker-Planck equation. The pseudo-Hamiltonian is transformed into a Coulomb-gas Hamiltonian, which, via the renormalization-group technique, leads to the Kosterlitz-Thouless transition.