Journal of Statistical Physics· 2026Q2· Review
A Survey on Rigorous Results for the Dynamics of Periodic FPU Chains
- 0citations
- Q2SCImago
- 2026year
Short summary
This review surveys rigorous analytic results on the dynamics of periodic Fermi-Pasta-Ulam (FPU) chains, highlighting connections to the Toda system and KdV equations, and presenting findings on thermalization times.
AI-generated from the title and abstract; the full text is not read.
Key points
- Analytic results on the dynamics of periodic FPU chains are reviewed.
- Connections are drawn between FPU and Toda Hamiltonians, yielding stability properties for FPU.
- The continuous limit of the Toda chain is shown to be described by KdV equations.
- The FPU system's dynamics are Hamiltonian and closely related to KdV hierarchy functions.
- In the thermodynamic limit, slow decay of autocorrelation functions implies lower bounds on thermalization times.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract In this paper we review some analytic results on the dynamics of the FPU system. In the first part of the paper, having in mind that the FPU Hamiltonian and the Toda Hamiltonian are close to each other, we present some results on the action angle variables of the Toda system and deduce some stability properties for the dynamics of the FPU system. We first focus on the case of finitely many particles and then we study the limit $$N\rightarrow \infty $$ N → ∞ . We also present some results on the continuous limit of the Toda chain showing that it is well described by a couple of KdV equations. Then we study directly the dynamics of the function interpolating the FPU system and show that the dynamics is Hamiltonian and that the Hamiltonian is very close to a function of the first three Hamiltonians of the KdV hierarchy. In the second part of the paper we present some results valid in the thermodynamic limit, according to which the time auto correlation functions of some suitably constructed observables decay slowly implying lower bounds on the thermalization times of the system.
The authors' abstract, as published at the source. Journal of Statistical Physics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Mathematical Physics
Mathematical PhysicsMathematics