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arXiv · 2605.24467

The peculiar response of Kelvin-Voigt chains with a free end

Rupayan Saha·Matthias Krüger
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Abstract

We exactly solve a model of a heterogeneous chain of overdamped, harmonically coupled particles with momentum-conserving dissipation. Despite being governed by a non-symmetric drift operator, the system admits an analytical diagonalization by use of a forward-difference transformation. In case of one free end, the response matrix shows a peculiar staircase form: the response of particle $i$ to a force acting on particle $j$ is independent of the properties and the length of the chain-part between $i$ and $j$. For rank-deficient interaction matrices, the state space is decomposed into free and constrained subspaces. We demonstrate that this separation has clear physical consequences: the free subspace governs steady state responses, while the constraint subspace governs the relaxation after cessation of forcing. We further show that a Maxwell chain arises as a singular limiting topology of the Kelvin-Voigt chain. These results establish a framework for analyzing heterogeneous overdamped dynamics with momentum conservation.

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Rupayan Saha, Matthias Krüger. 2026-05-23. The peculiar response of Kelvin-Voigt chains with a free end. https://doi.org/10.1088/1751-8121%2Fae8b46

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