Extensive packet excitations in FPU and Toda lattices

Christodoulidi, Helen (2017) Extensive packet excitations in FPU and Toda lattices. Europhysics Letters (EPL), 119 (4). p. 40005. ISSN 0295-5075

Full content URL: http://doi.org/10.1209/0295-5075/119/40005


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At low energies, the excitation of low-frequency packets of normal modes in the Fermi-Pasta-Ulam (FPU) and in the Toda model leads to exponentially localized energy profiles which resemble staircases and are identified by a slope σ that depends logarithmically on the specific energy ε=E/N . Such solutions are found to lie on stable lower-dimensional tori, named q-tori. At higher energies there is a sharp transition of the system's localization profile to a straight-line one, determined by an N-dependent slope of the form σ ~ (εN)^(-d) , d > 0. We find that the energy crossover between the two energy regimes decays as 1/N , which indicates that q-tori disappear in the thermodynamic limit. Furthermore, we focus on the times that such localization profiles are practically frozen and we find that these "stickiness times" can rapidly and accurately distinguish between a power-law and a stretched exponential dependence in 1/ε.

Keywords:Nonlinear dynamics and chaos, Classical statistical mechanics, Localized modes
Subjects:F Physical Sciences > F340 Mathematical & Theoretical Physics
G Mathematical and Computer Sciences > G121 Mechanics (Mathematical)
G Mathematical and Computer Sciences > G120 Applied Mathematics
Divisions:College of Science > School of Mathematics and Physics
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ID Code:37012
Deposited On:16 Sep 2019 09:58

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