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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 kind 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 wavevector 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.PACS numbers: 45.05.+x, 46.55.+d, 46.40.Ff The possibility of measuring friction at the atomic level provided by the Lateral Force Microscopes [1] and Quartz Crystal Microbalance [2] has stimulated intense research on this topic [3]. Phonon excitations are the dominant cause of friction in many cases [4]. Most studies are carried out for one-dimensional non-linear lattices [5][6][7][8][9][10][11][12] and in particular for the Frenkel-Kontorova (FK) model [13], where the surface layer is modeled by a harmonic chain and the substrate is replaced by a rigid periodic modulation potential. The majority [6][7][8][9][10][11][12] examines the steady state of the dynamical FK model in presence of dissipation representing the coupling of phonons to other, undescribed degrees of freedom.We study the dynamics of an undriven incommensurate FK chain. Our aim is to ascertain whether the experimentally observed superlubricity [14] can be due to the blocking of the phonon channels caused by an incommensurate contact of the two sliding surfaces. Therefore we do not include any explicit damping of the phonon modes, since we wish to find out if they can be excited at all by the motion of the center of mass (CM). In an earlier study, Shinjo and Hirano [5] found a superlubric regime for this model, where the chain would slide indefinitely without dynamic friction but with a recurrent exchange of kinetic energy between CM and a single internal mode. We will show that their finding is oversimplified by either too short simulation times or too small system sizes. The inherent non-linear coupling of the CM to the phonons leads to an irreversible decay of the CM velocity, albeit with very long time scales in some windows. The dissipative mechanism is driven by the coupling of the CM to the modes with modulation wavevector q or its harmonics, ω nq , and consists in a novel kind of parametric resonances with much wider windows of instabilities than those deriving from the standard Mathieu equation [15]. The importance of harmonic resonances at ω nq has been pointed out before [6,8,10], with the suggestion [10] that they could be absent in finite systems due to the discreteness of the phonon spectrum. However, it has not been realized that they act as a driving term for the onset of dissipation via subsequent complex parametric excitations which we shall describe, establishing quantitative estimates for their existence in ...

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