Chaos in FPUT-like Systems

The celebrated Fermi–Pasta–Ulam–Tsingou (FPUT) paradox refers to the apparent nonergodic behavior observed in a one-dimensional chain of oscillators with non-linear coupling. When initialized in a long wavelength mode, the system is seen to go through a long period of recurrent, quasi-periodic motion, which is believed to eventually thermalize. Recently, it has been proposed that the adiabatic gauge potential (AGP) serves as a probe for chaos in both classical and quantum systems1. In this work we apply such AGP techniques to classical FPUT and FPUT-like systems to understand their approach towards thermalization. Further, we study the AGP and the fidelity susceptibility over periodic orbits of the system. We compare results between FPUT and Toda systems in order to shed light on the differences between integrable and non-integrable models.

References

[1] C. Lim, K. Matirko, A. Polkovnikov, and M. O. Flynn. Defining classical and quantum chaos through adiabatic transformations, 2024.