Target Searches of Interacting Brownian Particles

We study the target search of interacting Brownian particles in a finite domain, focusing on the effect of inter-particle interactions on the search time. We derive the integral equation for the mean first-passage time and acquire its solution as a series expansion in the orders of the Mayer function. For dilute systems relevant to most target search problems, we analytically obtain the leading order correction to the search time and prove a universal relation given by the particle density and the second virial coefficient. Finally, we validate our theoretical prediction by Langevin dynamics simulations for the various types of the interaction potential.