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

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.

References in corpus (2)

• A momentum conserving model with anomalous thermal conductivity in low dimension
• Statistical mechanics of general discrete nonlinear Schr{ö}dinger models: Localization transition and its relevance for Klein-Gordon lattices

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• Condensation transition and ensemble inequivalence in the Discrete Nonlinear Schrödinger Equation
• Statistical mechanics of systems with long-range interactions and negative absolute temperature
• Effective mobility and diffusivity in coarsening processes
• Finite-size localization scenarios in condensation transitions
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
• Condensation induced by coupled transport processes
• Onsager coefficients in a coupled-transport model displaying a condensation transition
• Frozen dynamics of a breather induced by an adiabatic invariant
• First-order condensation transition in the position distribution of a run-and-tumble particle in one dimension
• Condensation with two constraints and disordered Discrete Non Linear Schrödinger breathers