A reduction scheme for coupled Brownian harmonic oscillators

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.

Automated summary

In this article, we propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We construct a lower dimensional model to reduce the description, which inherits some basic features of the original dynamics and is written in terms of suitable transport coefficients. The deterministic component of the dynamics is obtained using the invariant manifold method, while the diffusion terms are determined via the fluctuation-dissipation theorem. We focus on the behavior of the coefficients up to a critical value of the coupling parameter and discuss the commutativity of alternative reduction paths.