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 ${\mathrm{eR}}_{\mathrm{N}}{I}_c/{\epsilon }_c$ and $k_{B}T/{\epsilon }_c,$ where ${\epsilon }_c$ is the Thouless energy. Experimental and theoretical results are in excellent quantitative agreement.