Towards a derivation of fourier's law for coupled anharmonic oscillators
(2007) Communications in Mathematical Physics — Vol. 274, n° 3, p. 555-626 (2007)
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- Abstract
- We consider a Hamiltonian system made of weakly coupled anharmonic oscillators arranged on a three dimensional lattice Z(2n) x Z(2), and subjected to stochastic forcing mimicking heat baths of temperatures T-1 and T-2 on the hyperplanes at O 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 equilibrium state satisfying Fourier law that relates the heat current to a local temperature gradient. The temperature exhibits a nonlinear profile.
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Bricmont, J., & Kupiainen, A. (2007). Towards a derivation of fourier’s law for coupled anharmonic oscillators. Communications in Mathematical Physics, 274(3), 555-626. https://doi.org/10.1007/s00220-007-0284-5 (Original work published 2007)