Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains

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dc.creatorGershgorin, Boris
dc.creatorLvov, Yuri V.
dc.creatorCai, David
dc.date2007-03-26
dc.date.accessioned2026-07-07T07:53:56Z
dc.date.available2026-07-07T07:53:56Z
dc.descriptionThe dispersive interacting waves in Fermi-Pasta-Ulam (FPU) chains of particles in \textit{thermal equilibrium} are studied from both statistical and wave resonance perspectives. It is shown that, even in a strongly nonlinear regime, the chain in thermal equilibrium can be effectively described by a system of weakly interacting \textit{renormalized} nonlinear waves that possess (i) the Rayleigh-Jeans distribution and (ii) zero correlations between waves, just as noninteracting free waves would. This renormalization is achieved through a set of canonical transformations. The renormalized linear dispersion of these renormalized waves is obtained and shown to be in excellent agreement with numerical experiments. Moreover, a dynamical interpretation of the renormalization of the dispersion relation is provided via a self-consistency, mean-field argument. It turns out that this renormalization arises mainly from the trivial resonant wave interactions, i.e., interactions with no momentum exchange. Furthermore, using a multiple time-scale, statistical averaging method, we show that the interactions of near-resonant waves give rise to the broadening of the resonance peaks in the frequency spectrum of renormalized modes. The theoretical prediction for the resonance width for the thermalized $β$-FPU chain is found to be in very good agreement with its numerically measured value.
dc.identifierhttps://arxiv.org/abs/nlin/0703051
dc.identifierhttp://arxiv.org/abs/nlin/0703051
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126411
dc.subjectChaotic Dynamics
dc.titleInteractions of renormalized waves in thermalized Fermi-Pasta-Ulam chains
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