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

Autor:	Grava, T., Maspero, A., Mazzuca, G., Ponno, A.
Rok vydání:	2020
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs Nonlinear Sciences - Exactly Solvable and Integrable Systems
Zdroj:	Comm. Math. Phys. 380 (2020), no. 2, 811-851
Druh dokumentu:	Working Paper
DOI:	10.1007/s00220-020-03866-2
Popis:	We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by $N \gg 1$ particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $\beta^{-1}$. Given a fixed ${1\leq m \ll N}$, 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 $\beta$, 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. Comment: 36 pg
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2001.08070 Zobrazit plný text záznamu View this record from Arxiv