  We study coherent dynamics of two interacting Bose-Bose droplets by means of
the extended Gross-Pitaevskii equation. The relative motion of the droplets
couples to the phases of their components. The dynamics can be understood in
terms of the evolution of zero-energy modes recovering symmetries spontaneously
broken by the mean-field solution. These are translational symmetry and two
U(1) symmetries, associated with the phases of the droplets' two components. A
phase-dependent interaction potential and double Josephson-junction equations
are introduced to explain the observed variety of different scenarios of
collision. We show that the evolution of the droplets is a macroscopic
manifestation of the hidden dynamics of their phases. The occurrence of
nondissipative drag between the two supercurrents (Andreev-Bashkin effect) is
mentioned.
