Numerical simulation of microscopic thermalization in a one-dimensional harmonically trapped gas coupled to a chain of masses*

Many physical systems can be modeled as a large number of small, mobile particles coupled to a dissipative thermal bath. Ubiquitous phenomena such as Brownian motion, friction, and quantum back action can be analyzed in this framework. In this work, we construct a minimal experimentally-realizable model in which mobile particles are confined to a harmonic potential and coupled to a minimal thermal bath composed of a chain of coupled masses. Using a classical formulation, we show that, even when the mobile particles interact only with a single mass of the chain, they experience thermalization and drag. We derive general integro-differential equations of motion and apply them to several model systems. We study the scaling of model parameters, such as the relative masses of mobile and chain particles, the range, and the strength of the interaction. We also explore the effect of many mobile particles, as well as the timescale for the memory kernel in the interaction. This minimal model successfully captures thermal equilibration, where the energy distribution of the mobile particles approaches the expected Boltzmann form. The mobile particles' motion exhibits minimal cross-correlations, validating the independent particle approximation. Finally, we discuss several proposals for controllable experimental realizations of this model, including trapped ion chains, hybrid ion-atom systems, neutral atom bright solitons, and neutral atoms in an optical lattice.