Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential

Cedric Bernardin (1) , François Huveneers (2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study the thermal properties of a pinned disordered harmonic chain weakly perturbed by a noise and an anharmonic potential. The noise is controlled by a parameter λ → 0, and the anharmonicity by a parameter λ ≤ λ. Let κ be the conductivity of the chain, defined through the Green-Kubo formula. Under suitable hypotheses, we show that κ = O(λ) and, in the absence of anharmonic potential, that κ ∼ λ. This is in sharp contrast with the ordered chain for which κ ∼ 1/λ, and so shows the persistence of localization effects for a non-integrable dynamics

Domaines: Mécanique statistique [cond-mat.stat-mech]; Probabilités [math.PR]

Cedric Bernardin, François Huveneers. Small perturbation of a disordered harmonic chain by a noise and an anharmonic potential. Probability Theory and Related Fields, 2012, pp.1--31. ⟨10.1007/s00440-012-0458-8⟩. ⟨hal-00777266v1⟩