Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit
| Autor: | Tamara Grava, Alberto Maspero, Antonio Ponno, Guido Mazzuca |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Physical sciences
01 natural sciences Measure (mathematics) 010305 fluids & plasmas symbols.namesake FPUT lattice Mathematics - Analysis of PDEs 0103 physical sciences FOS: Mathematics Periodic boundary conditions 0101 mathematics Gibbs measure Adiabatic process Mathematical Physics Mathematical physics Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems 010102 general mathematics Order (ring theory) Adiabatic invariants Statistical and Nonlinear Physics Mathematical Physics (math-ph) Phase space Thermodynamic limit symbols Exactly Solvable and Integrable Systems (nlin.SI) Toda lattice Analysis of PDEs (math.AP) |
| Zdroj: | Grava, T, Maspero, A, Mazzuca, G & Ponno, A 2020, ' Adiabatic Invariants for the FPUT and Toda Chain in the Thermodynamic Limit ', Communications in Mathematical Physics, vol. 380, pp. 811–851 . https://doi.org/10.1007/s00220-020-03866-2 |
| 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: | OpenAIRE |
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