In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a wave packet due to interaction with and population of distant NMs. Eventually nonlinearity-induced frequency shifts take over and the wave packet becomes self-trapped. On finite chains a critical ramping speed is obtained, which separates delocalized final states from localized ones. The critical value depends on the strength of disorder and is largest when the localization length matches the system size.

• Received 11 September 2008
• Publisher error corrected 2 February 2009

DOI:https://doi.org/10.1103/PhysRevE.79.016217