Laboratoire de Physique Théorique
Toulouse - UMR 5152

Many-body systems in 1D display anomalous relaxation and transport proper- ties. For nonlinear lattices the anomalous feature amounts to the divergence of the finite-size heat conductivity κ(L) ∼ Lα in the limit L → ∞ and, corre- spondingly, to a nonintegrable decay of the equilibrium current-current corre- lator, J(t)J(0) ∼ t−(1−δ) for long times t → ∞. We present a self-consistent mode-coupling calculation for nonlinear lattices. We show that the asymptotic behaviour turns out to depend on the order of the leading nonlinearity in the interaction potential. We find that cubic and quartic nonlinearities are char- acterized by α = 1/3 and α = 1/2, respectively. Moreover numerical results, obtained for nonlinear lattices in condition of equilibrium and non-equilibrium, are compared with mode-coupling theory results.