Comparison between different methods of estimating of the relaxation times in the FPU model

TL;DR

This paper compares two indicators for equipartition in the FPU model and introduces a fast symplectic algorithm based on FFT for long-time integration.

Contribution

It demonstrates the equivalence of two equipartition indicators and proposes a novel fast symplectic integrator using FFT for efficient long-term simulations.

Findings

The two equipartition indicators yield essentially identical results.

The proposed FFT-based symplectic algorithm enables faster long-time integrations.

Abstract

After a brief review of the Fermi-Pasta-Ulam (FPU) conservative system of N nonlinearly coupled oscillators, this paper addresses two problems: first, comparing two indicators for the equipartition, showing that the results are essentially identical; second, finding a method that allows fast integration to reach the long integration times required in this area. In particular this work proposes a symplectic algorithm based on the Fast Fourier Transform.