Fate of Boltzmann's breathers: kinetic theory perspective

TL;DR

This paper investigates the dynamics of elastic particles in a harmonic trap, revealing persistent breathing modes at low density and their eventual decay due to finite-size effects and dissipation, supported by theoretical and simulation analysis.

Contribution

It provides a kinetic theory framework for understanding the breathing mode dynamics and their decay in confined elastic particle systems, including finite-density effects.

Findings

Breathing modes persist at low density and are characterized by specific initial conditions.

Finite particle size and dissipation lead to amplitude decay and frequency shifts.

Theoretical predictions agree well with Molecular Dynamics simulations for frequency shifts.

Abstract

The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach equilibrium except for highly specific initial conditions: it generically evolves towards and stays in a breathing mode. This state is periodic in time, with a Gaussian velocity distribution, an oscillating temperature and a density profile that oscillates as well. We characterize this breather in terms of initial conditions, and constants of the motion. For low but finite densities, the analysis requires to take into account the finite size of the particles. Under well-controlle approximations, a closed description is provided, which shows how equilibrium is reached at long times. The (weak) dissipation at work erodes the breather's amplitude, while concomitantly shifting its oscillation frequency. An excellent agreement is found between Molecular Dynamics simulation results and the theoretical predictions for the frequency shift. For the damping time, the agreement is not as accurate as for the frequency and the origin of the discrepancies is discussed.