Dissipation and thermalization in 1D systems with nonlinear bath coupling*

One of the big outstanding challenges for this technology is understanding the fundamental mechanisms of ion transport. There are two main pathways to studying this problem. On one hand, microscopic Molecular Dynamics (MD) simulations make it possible to explore the system behavior on very short time scales, tracking individual atoms to analyze the details of their motion. Unfortunately, extending the time of these highly realistic simulations comes at a very high computational cost. On the other hand, using the Langevin equation gives insight to the long-time limit, but at the cost of disconnecting microscopic details from macroscopic parameters like drag. The work proposes a simplified framework where the link between microscopic motion and the emergence of macroscopic quantities is clearer. 

A key feature that sets ionic drag in crystals apart from dissipative motion in fluids is the long-range order in crystalline systems. This order, along with the comparable masses of the mobile and medium particles is expected to introduce additional correlations, both spatial and temporal, in the particle-medium interactions. The simplicity of the system allows us to treat it in a non-Markovian way, making it possible to explore the phenomena that depend on long-time correlations. 

We study a simple system, where a mobile particle, constrained to move in one dimension, interacts with an infinitely long chain of masses connected by identical springs. When the particle is launched along the chain, it dissipates energy and, eventually, becomes trapped in one of the energy minima, as expected. Our analytic and numerical results demonstrate that the drag experienced by the particle due to its interaction with the chain exhibits a non-monotonic dependence on the particle speed, vanishing at high speeds. Analytics predict that including bias in the system to compensate for the energy loss due to drag can give rise to several distinct steady-state drift velocities, a fact confirmed by simulations. Due to our model’s simplicity, we can show how the system parameters impact the dissipation rate.