Abstract
AbstractWe consider the Fermi–Pasta–Ulam–Tsingou (FPUT) chain composed by $$N \gg 1$$
N
≫
1
particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $$\beta ^{-1}$$
β
-
1
. Given a fixed $${1\le m \ll N}$$
1
≤
m
≪
N
, we prove that the first m integrals of motion of the periodic Toda chain are adiabatic invariants of FPUT (namely they are approximately constant along the Hamiltonian flow of the FPUT) for times of order $$\beta $$
β
, for initial data in a set of large measure. We also prove that special linear combinations of the harmonic energies are adiabatic invariants of the FPUT on the same time scale, whereas they become adiabatic invariants for all times for the Toda dynamics.
Funder
H2020 Marie Sklodowska-Curie Actions
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Statistical and Nonlinear Physics
Cited by
9 articles.
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