An averaging theorem for FPU in the thermodynamic limit

Abstract

Consider an FPU chain composed of $N\gg 1$ particles, and endow the phase space with the Gibbs measure corresponding to a small temperature ${\beta }^{-1}$. Given a fixed $K<N$, we construct $K$ packets of normal modes whose energies are adiabatic invariants (i.e., are approximately constant for times of order ${\beta }^{1-a}$, $a>0$) for initial data in a set of large measure. Furthermore, the time autocorrelation function of the energy of each packet does not decay significantly for times of order $\beta$. The restrictions on the shape of the packets are very mild. All estimates are uniform in the number $N$ of particles and thus hold in the thermodynamic limit $N\to \infty$, $\beta >0$.

References in corpus (3)

• Counterpropagating Two-Soliton Solutions in the FPU Lattice
• An extensive adiabatic invariant for the Klein-Gordon model in the thermodynamic limit
• A series expansion for the time autocorrelation of dynamical variables

Cited by in corpus (9)

• Birkhoff coordinates for the Toda Lattice in the limit of infinitely many particles with an application to FPU
• Adiabatic invariants for the FPUT and Toda chain in the thermodynamic limit
• Memory effects in the Fermi-Pasta-Ulam Model
• An extensive resonant normal form for an arbitrary large Klein-Gordon model
• Chopping time of the FPU $\alpha$-model
• Some analytic results on the FPU paradox
• Freezing of the optical--branch energy in a diatomic FPU chain
• Prethermalization and conservation laws in quasi-periodically-driven quantum systems
• A large probability averaging Theorem for the defocousing NLS