A reduction scheme for coupled Brownian harmonic oscillators

Matteo Colangeli*, Manh Hong Duong, Adrian Muntean

*Corresponding author for this work

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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.
Original languageEnglish
Article number505002
Number of pages24
JournalJournal of Physics A: Mathematical and Theoretical
Issue number50
Publication statusPublished - 22 Dec 2022


  • model reduction
  • Markov processes
  • invariant manifold
  • fluctuation-dissipation theorem


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