Energy transfer dynamics and thermalization of two oscillators interacting via chaos

TL;DR

This paper investigates how two harmonic oscillators interact indirectly through a common chaotic environment, revealing conditions for thermalization and energy transfer dynamics.

Contribution

It introduces a model of two oscillators coupled via a chaotic environment and analyzes their equilibrium and thermalization behavior.

Findings

Equilibrium is reached for both particles and environment at long times.

A temperature can be assigned only when the environment size N is large.

Resonance conditions enable indirect coupling between particles.

Abstract

We consider the classical dynamics of two particles moving in harmonic potential wells and interacting with the same external environment (HE), consisting of N non-interacting chaotic systems. The parameters are set so that when either particle is separately placed in contact with the environment, a dissipative behavior is observed. When both particles are simultaneously in contact with HE an indirect coupling between them is observed only if the particles are in near resonance. We study the equilibrium properties of the system considering ensemble averages for the case N=1 and single trajectory dynamics for N large. In both cases, the particles and the environment reach an equilibrium configuration at long times, but only for large N a temperature can be assigned to the system.