The Metastable State of the FPUT Problem*

We study the approach to equilibrium in the Fermi-Pasta-Ulam-Tsingou (FPUT) problem of a chain of non-linearly coupled oscillators. It is expected that the presence of these nonlinear interactions leads to a quick equipartition through the exchange of energy between different modes of the system. However, it is observed that at low to intermediate energies the system can get trapped in a far-from-equilibrium ”metastable” state which can persist for a very long time. The trajectory of the system in the phase space is found to pass through stable regions around q-breathers [1], which are periodic states of the system localized in the mode space. Comparing these q-breather states to cnoidal wave solutions of the Toda lattice [2], we show that they are composed of quasi-solitons. We further explore this sea of periodic orbits, both stable and unstable, and attempt to establish thresholds on the energy and the nonlinearity below which the system does not reach equilibrium.

References

[1] S. Flach, M. V. Ivanchenko, and O. I. Kanakov. q-breathers and the fermi-pasta-ulam problem. Phys. Rev. Lett., 95:064102, Aug 2005.

[2] B. S. Shastry and A. P. Young. Dynamics of energy transport in a toda ring. Phys. Rev. B, 82:104306, Sep 2010.