THERMAL CONDUCTIVITY OF THE TODA LATTICE WITH CONSERVATIVE NOISE

Abstract. 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) ~ n^α, 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.

Keywords: Thermal conductivity, Toda lattice, anomalous heat transport, Fourier's law, nonequilibrium systems.