A study describes single-file diffusion of charged particles confined in a periodic potential exhibiting a devil’s staircase, the fractal structure of commensurate steps that appears in driven systems. In this regime, the particles move one behind another without being able to overtake each other, so their collective motion is reduced to one dimension and their diffusive dynamics is strongly modulated by the geometry of the potential.

The devil’s staircase is a classic object of nonlinear physics: it emerges when two length scales of the problem are incommensurate, and in it the locked phases occupy parameter intervals forming a Cantor set. The work analyses how this structure of successive locks affects the transport of the confined charged particles, showing that diffusion is not uniform but changes character depending on the region of the staircase in which the system sits.

The authors combine simulation and theoretical analysis to characterise the mean squared displacement of the particles as a function of time and of the potential’s control parameter. The results show that diffusion is restricted in the locked regions of the staircase and partially recovered in the sliding regions, with behaviours that interpolate between normal transport and subdiffusion depending on the degree of commensurability.

The relevance of the work lies in connecting two topics usually treated separately: one-dimensional transport of interacting particles and the physics of devil’s staircases. The resulting framework may be useful to describe ions in optical traps, charged colloids in narrow channels or vortices in superconductors, systems where geometric confinement and Coulomb interactions compete and where the fractal structure of the potential leaves a measurable imprint on diffusion.