Understanding the FPU state in FPU-like models

Understanding the FPU state in FPU-like models

Blog Article

Many papers investigated, in a variety of ways, the so-called "FPU state" in the Fermi-Pasta-Ulam model, namely the state, intermediate between the initial state and equipartition, that the system soon reaches if initially one or a few long-wavelength normal modes are excited.The FPU state has been observed, in particular, to obey a few characterizing Tools scalings laws.The aim of this paper is twofold: First, reviewing and commenting the literature on the FPU state, suggesting a possible way to organize it.Second, contributing to a better understanding of the FPU state by studying the similar Laser and party lighting state in the Toda model, which provides, as is known, the closest integrable approximation to FPU.As a new tool, we analyze the dimensionality of Toda invariant tori in states corresponding to the FPU state, and observe it obeys the main scaling law characterizing the FPU state.