Onset of sliding friction in incommensurate systems

We study the dynamics of an incommensurate chain sliding on a periodic lattice, modeled by the Frenkel-Kontorova Hamiltonian with initial kinetic energy, without damping and driving terms. We show that the onset of friction is due to a novel type of dissipative parametric resonances, involving several resonant phonons which are driven by the (dissipationless) coupling of the center of mass motion to the phonons with the wave vector related to the modulating potential. We establish quantitative estimates for their existence in finite systems and point out the analogy with the induction phenomenon in Fermi-Ulam-Pasta lattices.