Christodoulidi, H and Efthymiopoulos, C. and Bountis, T. (2010) Energy localization onqtori, longterm stability, and the interpretation of FermiPastaUlam recurrences. Physical Review E, 81 (1). ISSN 24700045
Full content URL: http://doi.org/10.1103/PhysRevE.81.016210
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
We focus on two approaches that have been proposed in recent years for the explanation of the socalled FermiPastaUlam (FPU) paradox, i.e., the persistence of energy localization in the “lowq” Fourier modes of FermiPastaUlam nonlinear lattices, preventing equipartition among all modes at low energies. In the first approach, a lowfrequency 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 “qtori” representing exponentially localized solutions on lowdimensional tori and use their stability properties to reconcile these two approaches and provide a more complete explanation of the FPU paradox.
Keywords:  FermiPastaUlam, lowdimensional tori, energy localization, PoincaréLindstedt method 

Subjects:  G Mathematical and Computer Sciences > G120 Applied Mathematics G Mathematical and Computer Sciences > G121 Mechanics (Mathematical) F Physical Sciences > F340 Mathematical & Theoretical Physics 
Divisions:  College of Science > School of Mathematics and Physics 
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ID Code:  37112 
Deposited On:  16 Sep 2019 10:17 
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