  We study the conservative and deterministic dynamics of two nonlinearly
interacting particles evolving in a one-dimensional spatially periodic
washboard potential. A weak tilt of the washboard potential is applied biasing
one direction for particle transport. However, the tilt vanishes asymptotically
in the direction of bias. Moreover, the total energy content is not enough for
both particles to be able to escape simultaneously from an initial potential
well; to achieve transport the coupled particles need to interact
cooperatively. For low coupling strength the two particles remain trapped
inside the starting potential well permanently. For increased coupling strength
there exists a regime in which one of the particles transfers the majority of
its energy to the other one, as a consequence of which the latter escapes from
the potential well and the bond between them breaks. Finally, for suitably
large couplings, coordinated energy exchange between the particles allows them
to achieve escapes -- one particle followed by the other -- from consecutive
potential wells resulting in directed collective motion. The key mechanism of
transport rectification is based on the asymptotically vanishing tilt causing a
symmetry breaking of the non-chaotic fraction of the dynamics in the mixed
phase space. That is, after a chaotic transient, only at one of the boundaries
of the chaotic layer do resonance islands appear. The settling of trajectories
in the ballistic channels associated with transporting islands provides
long-range directed transport dynamics of the escaping dimer.
