Thermal Conductivity of the Toda Lattice with Conservative Noise

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 gamma. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length n of the chain according to kappa(n)similar to n (alpha) , with 0 <alpha a parts per thousand currency sign1/2. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent alpha of the divergence depends on gamma.