Burgers equation and the Fermi-Pasta-Ulam-Tsingou lattice

The study of the thermalisation process in isolated systems is of broad interest. It was pioneered by Fermi-Pasta-Ulam-Tsingou (FPUT), who discovered the “paradoxical” absence of thermalisation in a one-dimensional lattice of coupled nonlinear oscillators. In this talk I will present a new avenue towards the understanding of thermalisation, the presence of a power-law in the Fourier energy spectrum. A universal scaling exponent is obtained by mapping the FPUT model onto a pair of Burgers equations. Energy is transferred to higher Fourier modes like in “Burgers turbulence”, while “shocks” develop on the lattice, and only at much longer times the system reaches energy equipartition. I will also present new numerical results where packets of Fourier modes are initially excited.

References
-M. Gallone, M. Marian, A. Ponno and S. Ruffo:"Burgers turbulence in the FPUT chain", Phys. Rev. Lett. 114101 (2023)
-M. Gallone, A. Ponno and S. Ruffo:"Energy cascade and Burgers turbulence in the FPUT chain", Phys. Rev. E, 054212 (2024)
-E. Druais, M. Gallone, A. Ponno and S. Ruffo: work in progress (2025)