We study conversion of thermal energy to mechanical energy and vice versa in an $\alpha$-Fermi-Pasta-Ulam-Tsingou (FPUT) chain with a spatially sinusoidal profile of initial temperature. We show analytically that coupling between macroscopic dynamics and quasiballistic heat transport gives rise to mechanical vibrations with growing amplitude. This phenomenon is referred to as ballistic resonance. At large times, these mechanical vibrations decay monotonically, and therefore the well-known FPUT recurrence paradox occurring at zero temperature is eliminated at finite temperatures.

• Received 6 December 2019
• Accepted 19 February 2020

DOI:https://doi.org/10.1103/PhysRevE.101.042209