Dissipative Currents in Superfluid 3He Weak Links

We calculate the current-pressure relation for pinholes connecting two volumes of bulk superfluid 3He-B. The theory of multiple Andreev reflections, adapted from superconducting weak links, leads to a nonlinear dependence of the dc current on pressure bias. In arrays of pinholes one has to take into account oscillations of the texture at the Josephson frequency. The associated radiation of spin waves from the junction leads to an additional dissipative current at small biases, in quantitative agreement with measurements.