A reduction scheme for coupled Brownian harmonic oscillators

TL;DR

This paper introduces a reduction scheme for coupled Brownian harmonic oscillators, simplifying their dynamics into a lower-dimensional model that retains key features, using invariant manifold and fluctuation-dissipation principles.

Contribution

It presents a novel reduction method combining invariant manifold and fluctuation-dissipation approaches for coupled Brownian oscillators.

Findings

Reduction valid up to a critical coupling strength

Behavior of transport coefficients analyzed near critical coupling

Weak coupling regime studied in detail

Abstract

We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original dynamics and is written in terms of suitable transport coefficients. The proposed procedure is twofold: while the deterministic component of the dynamics is obtained by a direct application of the invariant manifold method, the diffusion terms are determined via the Fluctuation-Dissipation Theorem. We highlight the behavior of the coefficients up to a critical value of the coupling parameter, which marks the endpoint of the interval in which a contracted description is available. The study of the weak coupling regime is addressed and the commutativity of alternative reduction paths is also discussed.