2009/12/08 by Helen Christodoulidi, H. Christodoulidi, Christos Efthymiopoulos +3
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Computer science #Equipartition theorem #Excited state #Exponential function #Fermi Gamma-ray Space Telescope #Fourier transform #Geometry #Lattice (music) #Linear stability #Magnetic field #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #Stability (learning theory) #Torus #nlin.CD
paper · pdf · doi:10.1103/physreve.81.016210
38 pages, 7 figures
arxiv created 2009/12/08 · openalex publication_date 2010/01/19 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We focus on two approaches that have been proposed in recent years for the explanation of the so-called Fermi-Pasta-Ulam (FPU) paradox, i.e., the persistence of energy localization in the "low-q " Fourier modes of Fermi-Pasta-Ulam nonlinear lattices, preventing equipartition among all modes at low energies. In the first approach, a low-frequency fraction of the spectrum is initially excited leading to the formation of "natural packets" exhibiting exponential stability, while in the second, emphasis is placed on the existence of "q breathers," i.e., periodic continuations of the linear modes of the lattice, which are exponentially localized in Fourier space. Following ideas of the latter, we introduce in this paper the concept of " q-tori" representing exponentially localized solutions on low-dimensional tori and use their stability properties to reconcile these two approaches and provide a more complete explanation of the FPU paradox.