Tail resonances of FPU q-breathers and their impact on the pathway to equipartition
arXiv:nlin/0610006 · doi:10.1063/1.2645141
Abstract
Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincare-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets.
References in corpus (3)
Cited by in corpus (10)
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- Boundary effects on quantum q-breathers in a Bose-Hubbard chain
- Periodic orbits, localization in normal mode space, and the Fermi-Pasta-Ulam problem
- q-breathers in Discrete Nonlinear Schroedinger lattices
- Elliptic tori in FPU non-linear chains with a small number of nodes
- Periodic Orbits in Fermi-Pasta-Ulam-Tsingou Systems
- Analysis of classical phase space and energy transfer for two rotating dipoles in an electric field
- Extensive packet excitations in FPU and Toda lattices
- Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou High-Dimensional Trajectories Through Manifold Learning: A Linear Approach