The Josephson critical current in a long mesoscopic S-N-S junction

We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal (N) embedded between two superconducting electrodes (S). Our experiments are performed on Nb-Cu-Nb junctions with highly-transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short and the long junction regimes and provide the temperature dependence of the critical current using dimensionless units $eR_{N}I_{c}/\epsilon_{c}$ and $k_{B}T/\epsilon_{c}$ where $\epsilon_{c}$ is the Thouless energy. Experimental and theoretical results are in excellent quantitative agreement.