Renormalized dispersion relations of β -Fermi-Pasta-Ulam chains in equilibrium and nonequilibrium states

Shi Xiao W Jiang, Hai Hao Lu, Douglas Zhou, David Cai

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We study the nonlinear dispersive characteristics in β-Fermi-Pasta-Ulam (FPU) chains in both thermal equilibrium and nonequilibrium steady state. By applying a multiple scale analysis to the FPU chain, we analyze the contribution of the trivial and nontrivial resonance to the renormalization of the dispersion relation. Our results show that the contribution of the nontrivial resonance remains significant to the renormalization, in particular, in strongly nonlinear regimes. We contrast our results with the dispersion relations obtained from the Zwanzig-Mori formalism and random phase approximation to further illustrate the role of resonances. Surprisingly, these theoretical dispersion relations can be generalized to describe dispersive characteristics well at the nonequilibrium steady state of the FPU chain with driving-damping in real space. Through numerical simulation, we confirm that the theoretical renormalized dispersion relations are valid for a wide range of nonlinearities in thermal equilibrium as well as in nonequilibrium steady state. We further show that the dispersive characteristics persist in nonequilibrium steady state driven-damped in Fourier space.

Original languageEnglish (US)
Article number032925
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number3
StatePublished - Sep 30 2014

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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