We consider $d$-dimensional chains of (an)harmonic oscillators we perturb by a noise conserving energy or energy and momentum. We review the thermal conduction properties we obtained for these systems and conclude by several open questions.
Studies of thermal conductivity in Fermi-Pasta-Ulam like lattices
On the approach to equilibrium of an Hamiltonian chain of anharmonic oscillators
Ising chain: Thermal conductivity and first-principle validation of Fourier law
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