Unbinding transition of probes in single-file systems

Single-file transport, arising in quasi one-dimensional geometries where particles cannot pass each other, is characterized by the anomalous dynamics of a probe, notably its response to an external force. In these systems, the motion of several probes submitted to different external forces, although relevant to mixtures of charged and neutral or active and passive objects, remains unexplored. Here, we determine how several probes respond to external forces. We rely on a hydrodynamic description of the symmetric exclusion process to obtain exact analytical results at long times. We show that the probes can either move as a whole, or separate into two groups moving away from each other. In between the two regimes, they separate with a different dynamical exponent, as $t^{1/4}$. This unbinding transition also occurs in several continuous single-file systems and is expected to be observable.