Hysteretic depinning of a particle in a periodic potential: Phase diagram and criticality

Víctor H. Purrello, José L. Iguain, Vivien Lecomte, Alejandro B. Kolton 

Links:  arxiv, PRE 2020

We consider a massive particle driven with a constant force in a periodic potential and subjected to a dissipative friction. As a function of the drive and damping, the phase diagram of this paradigmatic model is well known to present a pinned, a sliding, and a bistable regime separated by three distinct bifurcation lines. In physical terms, the average velocity v of the particle is nonzero only if either (i) the driving force is large enough to remove any stable point, forcing the particle to slide, or (ii) there are local minima but the damping is small enough, below a critical damping, for the inertia to allow the particle to cross barriers and follow a limit cycle; this regime is bistable and whether v>0 or v=0 depends on the initial state. In this paper, we focus on the asymptotes of the critical line separating the bistable and the pinned regimes. First, we study its behavior near the "triple point" where the pinned, the bistable, and the sliding dynamical regimes meet. 









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