Using tensor network states to describe periodically driven multiparticle Brownian ratchets

Single-particle Brownian ratchets have been thoroughly studied, but ratcheting phenomena in interacting many-body systems offer new challenges. Even with interactions as simple as volume exclusion, the mean steady-state current tends to respond dramatically to changes in carrier density. We present a novel approach for computing these currents for a time-periodic 1D ratchet discretized on a periodic-boundary-condition lattice. The approach leverages the time-dependent variational principle (TDVP) method of evolving binary tree tensor network states to compute the response of steady-state currents to particle density, the frequency of the ratchet drive, and the diffusion constant governing thermal motion. The TDVP approximation is controllable, and provided the tensor network's maximal bond dimension is sufficiently large, we demonstrate agreement with brute force Gillespie sampling. The method shows promise for studying classical many-body stochastic systems subject to time-dependent external forces, particularly when rare fluctuations play a crucial role.