Dissipative dynamics of the Josephson effect in binary Bose-Einstein-condensed mixtures

The dissipative dynamics of a pointlike Josephson junction in binary Bose-Einstein-condensed mixtures is analyzed within the framework of the model of a tunneling Hamiltonian. The transmission of unlike particles across a junction is described by the different transmission amplitudes. The effective action that describes the dynamics of the phase differences across the junction for each of two condensed components is derived by employing the functional integration method. In the low-frequency limit the dynamics of a Josephson junction can be described by two coupled equations in terms of the potential energy and dissipative Rayleigh function using a mechanical analogy. The interplay between mass currents of each mixture component appears in the second-order term in the tunneling amplitudes due to the interspecies hybridizing interaction. The asymmetric case of the binary mixtures with different concentrations and order parameters is considered as well.