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We study theoretically the dc Josephson effect between two volumes ofsuperfluid 3He-B. We first discuss how the calculation of the current-phaserelationships is divided into a mesoscopic and a macroscopic problem. We thenanalyze mass and spin currents and the symmetry of weak links. In quantitativecalculations the weak link is assumed to be a pinhole, whose size is small incomparison to the coherence length. We derive a quasiclassical expression forthe coupling energy of a pinhole, allowing also for scattering in the hole.Using a selfconsistent order parameter near a wall, we calculate thecurrent-phase relationships in several cases. In the isotextural case, thecurrent-phase relations are plotted assuming a constant spin-orbit texture. Inthe opposite anisotextural case the texture changes as a function of the phasedifference. For that we have to consider the stiffness of the macroscopictexture, and we also calculate some surface interaction parameters. We analyzethe experiments by Marchenkov et al. We find that the observed pi states andbistability hardly can be explained with the isotextural pinhole model, but agood quantitative agreement is achieved with the anisotextural model.Comment: 20 pages, 21 figures, revtex

physical review. b, condensed matter

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Pinhole calculations of the Josephson effect in3He−B