Dynamics of soft interacting particles on a comb

We study the dynamics of overdamped Brownian particles interacting through soft pairwise potentials on a comb-like structure. Within the linearized Dean-Kawasaki framework, we characterize the particle density fluctuations by computing their one- and two-point correlation functions. For a tracer particle constrained to move along the comb backbone, we determine the spatial correlation profile between its position and the density of surrounding bath particles. Furthermore, we derive the correction to the diffusion coefficient of the tracer due to interactions with other particles, validating our results through numerical simulations.