Dimer motion on a periodic substrate: spontaneous symmetry breaking and absolute negative mobility

We consider two coupled particles moving along a periodic substrate potential with negligible inertia effects (overdamped limit). Even when the particles are identical and the substrate spatially symmetric, a sinusoidal external driving of appropriate amplitude and frequency may lead to spontaneous symmetry breaking in the form of a permanent directed motion of the dimer. Thermal noise restores ergodicity and thus zero net velocity, but entails arbitrarily fast diffusion of the dimer for sufficiently weak noise. Moreover, upon application of a static bias force, the dimer exhibits a motion opposite to that force (absolute negative mobility). The key requirement for all these effects is a nonconvex interaction potential of the two particles.