Anomalous energy transport in the FPU-β chain
نویسندگان
چکیده
منابع مشابه
Anomalous energy transport in FPU-β chain
This paper is devoted to the derivation of a macroscopic diffusion equation (Fourier’s law) describing the transport of energy in an anharmonic chain. More precisely, we study here the so-called FPU-β chain, which is a very simple model for a one-dimensional crystal in which atoms are coupled to their nearest neighbors by a harmonic potential, weakly perturbed by a quartic potential. The starti...
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We consider the energy current correlation function for the FPU-β lattice. For small non-linearity one can rely on kinetic theory. The issue reduces then to a spectral analysis of the linearized collision operator. We prove thereby that, on the basis of kinetic theory, the energy current correlations decay in time as t−3/5. It follows that the thermal conductivity is anomalous, increasing as N ...
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The evolution towards equipartition in the β-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally unstable and to give rise to a striking localization process. The spontaneously created excitations have strong similarity with moving exact breathers solutions. But th...
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The evolution towards equipartition in the β-FPU chain is studied considering as initial condition the highest frequency mode. Above an analytically derived energy threshold, this zone-boundary mode is shown to be modulationally unstable and to give rise to a striking localization process. The spontaneously created excitations have strong similarity with moving exact breathers solutions. But th...
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After a brief comprehensive review of old and new results on the well known Fermi-Pasta-Ulam (FPU) conservative system of N nonlinearly coupled oscillators, we present a compact linear mode representation of the Hamiltonian of the FPU system with quartic nonlinearity and periodic boundary conditions, with explicitly computed mode coupling coefficients. The core of the paper is the proof of the ...
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Mathematics
سال: 2008
ISSN: 0010-3640,1097-0312
DOI: 10.1002/cpa.20243