Minimal model of mobile particles interacting with an infinite one-dimensional lattice: dissipation, thermalization, drag, and diffusion

We explore the classical dynamics of mobile particles interacting with an infinite one-dimensional chain of harmonic oscillators (a 1D lattice). This effective model describes ionic conduction in anisotropic solid-state materials or molecular motion in nanotubes. Through a combination of analytic and numerical calculations, we show that, in the absence of thermal motion in the lattice, coupling to the lattice will dissipate the mobile particle's kinetic energy. This dissipation leads to drag that is nonmonotonic in the particle speed. Under a constant bias, this system exhibits multiple steady drift velocities, linking macroscopic transport to microscopic lattice properties. We discuss how thermal motion influences these properties, and how such a model could be implemented in a collection of trapped ions or neutral atoms to explore thermalization and transport in low-dimensional systems.