Cahiers du CEREMADE 

Unité
Mixte de Recherche du C.N.R.S. N°7534 

Abstract : We consider a system of harmonic oscillators perturbed by a stochastic dynamics conserving momentum and energy. We compute the effective
thermal conductivity via GreenKubo formula. In the limit as the size $N$
of the system goes to infinity, conductivity remains finite if a
pinning (on site potential) is present or in dimension $d\ge 3$. In
the unpinned case
conductivity diverges like $N$ in dimension 1 and like $\ln N$ in dimension 2.
Then we consider the open system in contact with 2 heat bath at
different temperature in the stationary state. We prove that the
conductivity of the open
system coincides with the GreenKubo formula, and
a corresponding Fourier's law in the cases of finite
conductivity. Mathematical complete proofs
of these results are in reference [1]. 





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