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A microscopic model for describing a superconducting mesoscopic weak link ispresented. We consider a model geometry consisting of a narrow channel coupledto wider superconducting electrodes which act as reservoirs fixing theasymptotic values of the complex order parameter. For this model, theBogoliubov-de Gennes equations are discretized and solved self-consistentlyusing a non-equilibrium Green functions formalism. The transport properties andthe electronic excitation spectra of this system are studied for the differentregimes that can be reached by varying parameters like coherence length,constriction length, normal transmission coefficient and temperature. We studyin detail the transition from the point contact limit to the infinite channellength case, analyzing the maximum Josephson current that can be sustained bythe weak link as a function of its transmission coefficient and length.Comment: 23 pages (RevTex) 11 figures available upon request  (fj@uamc10.fmc.uam.es

Self-consistent theory of superconducting mesoscopic weak links