  Ballistic transport and resonance phenomena are elucidated in the
one-dimensional $\alpha$-Fermi-Pasta-Ulam-Tsingou (FPUT) model using an
approach of computing thermal response functions. The existence of periodic
oscillations in spatially sinusoidal temperature profiles seen in previous
studies is confirmed. However, the results obtained using response functions
enable a more complete understanding. In particular, it is shown that resonance
involves beats between normal modes which tend to reinforce in a
one-dimensional chain. Anharmonic scattering acts to destroy phase coherence
across the statistical ensemble, and with increasing anharmonicity, transport
is driven towards the diffusive regime. These results provide additional
insight into anomalous heat transport in low-dimensional systems. Normal-mode
scattering is also explored using time correlation functions. Interestingly,
these calculations, in addition to demonstrating loss of phase coherence across
an ensemble of simulations, appear to show evidence of so-called q-breathers in
conditions of strong anharmonicity. Finally, we describe how the approach
outlined here could be developed to include quantum statistics and also also
first-principles estimates of phonon scattering rates to elucidate second sound
and ballistic transport in realistic materials at low temperatures.

Statistical Mechanics;Chaotic Dynamics