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Gap-controlled thermalization in a chain of alternating nonlinear springs: an SSH model version of the Fermi-Pasta-Ulam-Tsingou problem

Year: 2026
Type: preprint
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 $1\pmΔκ$, 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.
DOI: 10.48550/arxiv.2609.09498
Language: English
Open Access status: green
Award: G156748425
OpenAlex ID: W7212176099
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