Adiabatic invariants for the FPUT and Toda chains in the thermodynamic limit

14 July 2020
Tamara Grava
We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by N particles  on the line  and endowed the phase space with the Gibbs measure at temperature 1/beta. We prove that the   integrals of motion of the Toda chain  are adiabatic invariants for the FPTU chain for times of order beta. Further we prove that certain combination of the harmonic energies are adiabatic invariants  of the FPUT chain  on the same time scale, while they are adiabatic invariants for Toda chain for all times. Joint work with A. Maspero, G. Mazzuca and A. Ponno.
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