Résumé en anglais

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter γ . We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to κ(n) ∼ nα, with 0 < α ≤ 1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent α of the divergence depends on γ .