Gap-controlled thermalization in a chain of alternating nonlinear springs: an SSH model version of the Fermi-Pasta-Ulam-Tsingou problem
Abstract
In classical anharmonic lattices, the resonance structure driving nonlinear mode mixing is reshaped by band gaps. However, it remains unclear whether a spectral gap hinders or promotes long-time thermalization. Here we study a Fermi-Pasta-Ulam-Tsingou (FPUT) chain of equal masses joined by alternating dimensionless spring constants 1±Δκ, so that the chain is dimerized with strength Δκ, the classical vibrational analogue of the Su-Schrieffer-Heeger (SSH) model, and quantify how the acoustic-optical gap controls relaxation under α-type (cubic) nonlinearity. Tracking modal energies and spectral entropy via long-time symplectic simulations, we find that dimerization delays long-time relaxation. At Δκ=1/2, set by the onset of the first umklapp process that allows two zone-boundary acoustic phonons to fuse into a zone-center optical phonon, the three-wave acoustic-acoustic-optical channel closes. The effective acoustic-to-optical scattering rate reveals an interplay between the dynamic resonance vertex and the kinematic resonance manifold, which evolve differently with the dimerization parameter. Above the threshold Δκ=1/2, energy redistribution can nevertheless continue through higher-order resonances and quasiresonances. Yet specific boundary conditions and initial conditions can inhibit equipartition. These results identify the phononic gap as a tunable, momentum-selective filter for nonlinear energy transport, suggesting a general route to controlling energy transfer and equipartition in dimerized or topologically gapped nonlinear lattices and in flexible mechanical systems.
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BibTeX
@misc{ake2026gapcontrolled,
title = {{Gap-controlled thermalization in a chain of alternating nonlinear springs: an SSH model version of the Fermi-Pasta-Ulam-Tsingou problem}},
author = {José A. Aké and Gerardo G. Naumis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.09498},
eprint = {2609.09498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09498},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gap-controlled thermalization in a chain of alternating nonlinear springs: an SSH model version of the Fermi-Pasta-Ulam-Tsingou problem
AU - José A. Aké
AU - Gerardo G. Naumis
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2609.09498
UR - https://arxiv.org/abs/2609.09498
AB - In classical anharmonic lattices, the resonance structure driving nonlinear mode mixing is reshaped by band gaps. However, it remains unclear whether a spectral gap hinders or promotes long-time thermalization. Here we study a Fermi-Pasta-Ulam-Tsingou (FPUT) chain of equal masses joined by alternating dimensionless spring constants 1±Δκ, so that the chain is dimerized with strength Δκ, the classical vibrational analogue of the Su-Schrieffer-Heeger (SSH) model, and quantify how the acoustic-optical gap controls relaxation under α-type (cubic) nonlinearity. Tracking modal energies and spectral entropy via long-time symplectic simulations, we find that dimerization delays long-time relaxation. At Δκ=1/2, set by the onset of the first umklapp process that allows two zone-boundary acoustic phonons to fuse into a zone-center optical phonon, the three-wave acoustic-acoustic-optical channel closes. The effective acoustic-to-optical scattering rate reveals an interplay between the dynamic resonance vertex and the kinematic resonance manifold, which evolve differently with the dimerization parameter. Above the threshold Δκ=1/2, energy redistribution can nevertheless continue through higher-order resonances and quasiresonances. Yet specific boundary conditions and initial conditions can inhibit equipartition. These results identify the phononic gap as a tunable, momentum-selective filter for nonlinear energy transport, suggesting a general route to controlling energy transfer and equipartition in dimerized or topologically gapped nonlinear lattices and in flexible mechanical systems.
ER -