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

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

2007-03-26

arxiv.org/abs/nlin/0703051v1

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

The 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 $\beta$-FPU chain is found to be in very good agreement with its numerically measured value.

Affiliated with

Also associated with

No associations

Rating

Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interactions of renormalized waves in thermalized Fermi-Pasta-Ulam chains will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-68808