On the derivation of Fourier's law for coupled anharmonic oscillators

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dc.creatorBricmont, Jean
dc.creatorKupiainen, Antti
dc.date2006-05-22
dc.date.accessioned2026-07-07T07:13:46Z
dc.date.available2026-07-07T07:13:46Z
dc.descriptionWe study the Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice and subjected to a stochastic forcing mimicking heat baths of temperatures T_1 and T_2 on the hyperplanes at x_1=0 and N. We introduce a truncation of the Hopf equations describing the stationary state of the system which leads to a nonlinear equation for the two-point stationary correlation functions. We prove that these equations have a unique solution which, for N large, is approximately a local equlibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile.
dc.description69 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0605062
dc.identifierhttp://arxiv.org/abs/math-ph/0605062
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112594
dc.subjectMathematical Physics
dc.titleOn the derivation of Fourier's law for coupled anharmonic oscillators
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