Hysteresis in Dynamically Pinned Sliding States

We analyse the occurrence of bistability and hysteretical behavior in the underdamped motion of a simple one-dimensional lubricated friction model inspired by the tribological problem of two incommensurate sliding surfaces with a thin sheet interposed. This system was recently found to possess exact velocity plateaus for large parameters intervals, showing a remarkable quantization of the center-mass motion. We detail the dynamics of the pinned-unpinned transitions induced as an external dragging force is introduced in order to alter the stability of the dynamically pinned plateau. A critical threshold value F+↑ c of the adiabatically applied force Fext is required to disrupt the robust kink dynamics of the quantized state. The plateau is then recovered at much lower value F+↓ c of the external force thus producing a clear hysteresis loop that resembles to the hysteresis occuring in the transition from static to dynamic friction. Indeed, the pinned-unpinned transition is interpreted as a dynamic uncoupling of the chain density-fluctuations (solitons, due to lattice mismatch with one substrate) from the other substrate. We analyse the dependency of this hysteresis loop on the system parameters obtaining a phase diagram, characterized by a first-order transition tuning to a second-order line at a critical point. Advisor: Dr. Nicola Manini Co-Advisor: Dr. Andrea Vanossi