THERMAL CONDUCTIVITY OF THE TODA LATTICE WITH CONSERVATIVE NOISE
(with Frédéric Legoll, Stefano Olla and Gabriel Stoltz)
(with Frédéric Legoll, Stefano Olla and Gabriel Stoltz)
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.