Periodically-driven quantum systems can exhibit topologically non-trivial
behaviour, even when their quasi-energy bands have zero Chern numbers. Much
work has been conducted on non-interacting quantum-mechanical models where this
kind of behaviour is present. However, the inclusion of interactions in
out-of-equilibrium quantum systems can prove to be quite challenging. On the
other hand, the classical counterpart of hard-core interactions can be
simulated efficiently via constrained random walks. The non-interacting model
proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013)], has a special point
for which the system is equivalent to a classical random walk. We consider the
classical counterpart of this model, which is exact at a special point even
when hard-core interactions are present, and show how these quantitatively
affect the edge currents in a strip geometry. We find that the interacting
classical system is well described by a mean-field theory. Using this we
simulate the dynamics of the classical system, which show that the interactions
play the role of Markovian, or time dependent disorder. By comparing the
evolution of classical and quantum edge currents in small lattices, we find
regimes where the classical limit considered gives good insight into the
quantum problem.Comment: 15 pages, 15 figures, new content on the quantum mode
