The Subtle Road to Equilibrium in the FPUT Model

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• David K. Campbell (Boston University)
• Thursday 23 May 2019, 13:00-14:00
• MR14, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Anne Herrmann.

The interpretation and consequences of the celebrated Fermi, Pasta, Ulam, Tsingou (FPUT) numerical experiment have challenged scientists for more than six decades. The history of how the original FPUT discovery led to the theory of “solitons,” was key in the understanding of Hamiltonian chaos, and led to the birth of “nonlinear science” is well documented, but there are many fascinating details which are only now being explored and understood. In this presentation, I will discuss two recently studied examples: namely, the details of the existence and breakdown of recurrences and super-recurrences in both the alpha- and beta- versions of the FPUT system, and the remarkable intermittent dynamics, involving long-time, large deviations, that occur once the systems has nominally reached equilibrium.

In the first study [1], we find higher-order recurrences (HoR)s—which amount to “super-super-recurrences” in both the alpha and beta models. The periods of these HoR scale non-trivially with energy due to apparent singularities caused by nonlinear resonances, which differ in the two models. Further, the mechanisms by which the HoR breakdown differ strikingly in the two models.

In the second study [2], we find that the dynamics at equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to localized excitations in normal mode space (q-breathers). Measuring the exponent allows to predict the transition into nonergodic dynamics.

*Work in collaboration with Carlo Danielli, Sergej Flach, and Salvatore Pace.

[1] Salvatore D. Pace and David K. Campbell, “Behavior and Breakdown of Higher-Order-Fermi- Pasta-Ulam-Tsignou Recurrences,” arXiv:181100663 (Chaos, to appear)

[2] C. Danieli, D. K. Campbell, and S. Flach, “Intermittent many-body dynamics at equilibrium,” Phys. Rev. E 95 060202 (R) (2017).

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