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Ballistic transport and resonance phenomena are elucidated in theone-dimensional $\alpha$-Fermi-Pasta-Ulam-Tsingou (FPUT) model using anapproach of computing thermal response functions. The existence of periodicoscillations in spatially sinusoidal temperature profiles seen in previousstudies is confirmed. However, the results obtained using response functionsenable a more complete understanding. In particular, it is shown that resonanceinvolves beats between normal modes which tend to reinforce in aone-dimensional chain. Anharmonic scattering acts to destroy phase coherenceacross the statistical ensemble, and with increasing anharmonicity, transportis driven towards the diffusive regime. These results provide additionalinsight into anomalous heat transport in low-dimensional systems. Normal-modescattering is also explored using time correlation functions. Interestingly,these calculations, in addition to demonstrating loss of phase coherence acrossan ensemble of simulations, appear to show evidence of so-called q-breathers inconditions of strong anharmonicity. Finally, we describe how the approachoutlined here could be developed to include quantum statistics and also alsofirst-principles estimates of phonon scattering rates to elucidate second soundand ballistic transport in realistic materials at low temperatures.

Analysis of ballistic transport and resonance in the $\alpha$-Fermi-Pasta-Ulam-Tsingou model