Classical Dynamics of Harmonically Trapped Interacting Particles

TL;DR

This paper investigates the classical dynamics of a one-dimensional trapped gas with finite-range repulsive interactions, focusing on breathing mode behavior and thermalization processes, revealing non-monotonic frequency dependence and conditions for thermalization.

Contribution

It provides a detailed analysis of how interaction strength affects breathing modes and thermalization in a classical trapped gas, bridging insights to quantum gas dynamics.

Findings

Breathing frequency decreases then increases with interaction strength.

Thermalization occurs when interaction strength exceeds energy per particle.

Collision effects explain the non-monotonic frequency behavior.

Abstract

Motivated by current interest in the dynamics of trapped quantum gases, we study the microcanonical dynamics of a trapped one-dimensional gas of classical particles interacting via a finite-range repulsive force of tunable strength. We examine two questions which have been of interest in quantum dynamics: (1) the breathing mode (size oscillation) dynamics of the trapped gas and the dependence of the breathing frequency on the interaction strength, and (2) the long-time relaxation and possible thermalization of the finite isolated gas. We show that the breathing mode frequency has non-monotonic dependence on the magnitude of the mutual repulsion, decreasing for small interactions and increasing for larger interactions. We explain these dependences in terms of slowing-down or speeding-up effects of two-body collision processes. We find that the gas thermalizes within a reasonable finite timescale in the sense of single-particle energies acquiring a Boltzmann distribution, only when the interaction strength is large compared to the energy per particle.