Stochastic systems with Bose-Hubbard interactions: Effects of bias on particles on a random comb

We study stochastic transport of interacting particles on a disordered network described by the random comb geometry. The model is defined on a one-dimensional backbone from which branches of random lengths emanate, providing a minimal model of percolation networks beyond the critical percolation probability. The dynamics obeys local detailed balance with respect to a Bose-Hubbard Hamiltonian containing both an external bias and on-site repulsion. This choice yields an analytically tractable steady state through a mapping to the zero-range process. We compute the backbone current, branch density profiles, and macroscopic drift velocity, and analyze how bias and interactions compete to shape transport. The backbone current increases monotonically with density, while the drift velocity displays a nonmonotonic dependence on the external field, remaining finite for any nonzero bias, in contrast to the vanishing drift velocity of noninteracting particles beyond a threshold bias. Density profiles along branches exhibit stepwise plateaus governed by the ratio of interaction to bias energy. These results highlight how repulsive interactions suppress trapping and restore transport in disordered geometries, bridging earlier studies of field-induced drift in random networks with the physics of disordered Bose-Hubbard systems.