Recurrence in a periodically driven and weakly damped Fermi-Pasta-Ulam-Tsingou chain

TL;DR

The study shows that a periodically driven, weakly damped $\alpha$-FPUT chain can exhibit long-lived recurrence-like energy exchange among a few low-frequency modes in narrow parameter regions, challenging the expectation of rapid thermalization in multimode nonlinear systems. By numerically solving the driven-damped equations with fixed boundaries and tracking total and normal-mode energies, the authors map regions of recurrence in driving frequency, amplitude, and damping, and reveal a strong dependence on chain length. They identify a representative case with a recurrence period around $41.3\,T_{0}$ and demonstrate that recurrence windows narrow substantially as the system size grows, implying persistence in the thermodynamic limit is unlikely. The work draws a nuanced analogy to time-crystal behavior while establishing a distinct, non-symmetry-breaking form of long-time temporal order in driven open multimode lattices, with potential guidance for experimental realization of quasi-periodic states.

Abstract

We report numerical evidence of Fermi-Pasta-Ulam-Tsingou (FPUT)-like recurrence in weakly damped, periodically driven alpha-FPUT chains. In narrow regions of driving amplitude and damping, energy is quasi-periodically exchanged among a few low-frequency modes over long timescales. Unlike discrete time crystals, the recurrence period is not an integer multiple of the driving period and does not correspond to spontaneous symmetry breaking, yet it may suggests a generalized, relaxed form of time-crystalline-like order. The maximum damping allowing recurrence decreases rapidly with chain length, suggesting that in the thermodynamic limit such behavior is unlikely to persist. These results reveal a new type of coherent nonlinear dynamics in driven, open multimode systems and provide guidance for experimentally realizing long-lived quasi-periodic states.

Figures (7)

• Figure 1: (a) The FPUT recurrence in a chain of length $N = 32$ with $\alpha = 0.25$. (b) Multiple recurrence cycles are suppressed even when a small damping $\eta = 1\times10^{-4}$ is introduced.
• Figure 2: Representative recurrence phenomenon. (a--c) Simulation results for the $N = 8$ chain with $\eta = 2.5\times10^{-3}$, driving amplitude $F = 5\times10^{-3}$, and driving frequency $\omega = 0.347$ (close to the first mode $\omega_{1} = 0.3473$). The horizontal axis represents time in units of the driving period $T_0$. (d) Fast Fourier transform (FFT) of the steady-state response shown in panel (c).
• Figure 3: (a) Total energy spectra of the $N = 8$ chain as a function of the driving frequency near the first mode $\omega_{1} = 0.3473$, for different driving amplitudes. (b) The same data for $F = 5\times10^{-3}$ shown separately, with a linear scale on the vertical axis. (c) Enlarged view of the frequency range where the recurrence phenomena occur, obtained from a finer frequency scan of the section shown in (b). (d--f) Time-domain simulations for three representative driving frequencies.
• Figure 4: (a) Total energy spectra of the $N = 8$ chain as a function of the driving frequency from 0.32 to 2, for the driving amplitudes $F = 5\times10^{-3}$. Because the chain is driven uniformly, only modes with even spatial symmetry about the chain center are excited, so the primary resonance peaks appear only near the odd-numbered mode frequencies. (b) Spatial symmetry of the normal modes.
• Figure 5: (a) Total energy spectra of the $N = 8$ chain as a function of the driving frequency near the first mode $\omega_{1} = 0.3473$, for driving amplitudes $F = 10\times10^{-3}$. (b--d) Time-domain simulations for three representative driving frequencies.