Some analytic results on the FPU paradox

Abstract

We present some analytic results aiming at explaining the lack of thermalization observed by Fermi Pasta and Ulam in their celebrated numerical experiment. In particular we focus on results which persist as the number $N$ of particles tends to infinity. After recalling the FPU experiment and some classical heuristic ideas that have been used for its explanation, we concentrate on more recent rigorous results which are based on the use of (i) canonical perturbation theory and KdV equation, (ii) Toda lattice, (iii) a new approach based on the construction of functions which are adiabatic invariants with large probability in the Gibbs measure.

References in corpus (3)

• Birkhoff coordinates for the Toda Lattice in the limit of infinitely many particles with an application to FPU
• An averaging theorem for FPU in the thermodynamic limit
• Global Birkhoff coordinates for the periodic Toda lattice

Cited by in corpus (7)

• Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit
• Korteweg-de Vries and Fermi-Pasta-Ulam-Tsingou: asymptotic integrability of quasi unidirectional waves
• Metastability phenomena in two-dimensional rectangular lattices with nearest-neighbour interaction
• Chopping time of the FPU $\alpha$-model
• Analysis of classical phase space and energy transfer for two rotating dipoles in an electric field
• Hamiltonian field theory close to the wave equation: from Fermi-Pasta-Ulam to water waves
• A large probability averaging Theorem for the defocousing NLS