Spectral description of the dynamics of ultracold interacting bosons in disordered lattices

Benoît Vermersch (1) , Jean Claude Garreau (1)

1 PhLAM - Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523

We study the dynamics of a nonlinear one-dimensional disordered system from a spectral point of view. The spectral entropy and the Lyapunov exponent are extracted from the short time dynamics, and shown to give a pertinent characterization of the different dynamical regimes. The chaotic and self-trapped regimes are governed by log-normal laws whose origin is traced to the exponential shape of the eigenstates of the linear problem. These quantities satisfy scaling laws depending on the initial state and explain the system behaviour at longer times.

Mots clés: anderson localization; interactions; disordered systems; ultracold atoms

Domaines: Physique Quantique [quant-ph]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Dynamique Chaotique [nlin.CD]; Gaz Quantiques [cond-mat.quant-gas]

Benoît Vermersch, Jean Claude Garreau. Spectral description of the dynamics of ultracold interacting bosons in disordered lattices. New Journal of Physics, 2013, New Journal of Physics 15 (2013) 045030 (15pp). ⟨10.1088/1367-2630/15/4/045030⟩. ⟨hal-00762095⟩