The peculiar response of Kelvin-Voigt chains with a free end (opens in new tab)

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 pro...