Relaxation and coarsening of weakly-interacting breathers in a simplified DNLS chain

Stefano Iubini, Antonio Politi, Paolo Politi

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Abstract

The discrete nonlinear Schrödinger (DNLS) equation displays a parameter region characterized by the presence of localized excitations (breathers). While their formation is well understood and it is expected that the asymptotic configuration comprises a single breather on top of a background, it is not clear why the dynamics of a multi-breather configuration is essentially frozen. In order to investigate this question, we introduce simple stochastic models, characterized by suitable conservation laws. We focus on the role of the coupling strength between localized excitations and background. In the DNLS model, higher breathers interact more weakly, as a result of their faster rotation. In our stochastic models, the strength of the coupling is controlled directly by an amplitude-dependent parameter. In the case of a power-law decrease, the associated coarsening process undergoes a slowing down if the decay rate is larger than a critical value. In the case of an exponential decrease, a freezing effect is observed that is reminiscent of the scenario observed in the DNLS. This last regime arises spontaneously when direct energy diffusion between breathers and background is blocked below a certain threshold.
Original languageEnglish
Article number073201
Pages (from-to)1-21
Number of pages21
JournalJournal of statistical mechanics-Theory and experiment
Volume2017
Early online date12 Jul 2017
DOIs
Publication statusPublished - Jul 2017

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Keywords

  • diffusion
  • coarsening processes
  • stochastic particle dynamics

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