Study on two coupled relativistic superfluids with spontaneous symmetry breaking

In this Letter, we have studied two coupled relativistic superfluids with spontaneous U(1) symmetry breaking, using Poisson bracket technique. After constructing the commutators between thermo-quantities and field quantities, the equations of motion are obtained. These equations describe the system in the frame of two-constituent superfluid theory and provide a clear picture relating the symmetry breaking and the physical quantities explicitly. The interference effect is discussed and the Josephson-type equation is also given. Furthermore, the dissipation effect and entropy production mechanism are presented and the dissipative coefficients are given explicitly in the first-order theory framework