Universal Correlations and Dynamic Disorder in a Nonlinear Periodic 1D System

Abstract

When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when the system is nonlinear, correlations are spontaneously formed. We find that for strong nonlinearities, the intensity histograms approach a narrow Gaussian distributed around their mean and phase correlations are formed between neighboring sites. Sites tend to be out-of-phase for a positive nonlinearity and in-phase for a negative one. The field correlations take a universal shape independent of parameters. This nonlinear evolution produces an effectively dynamically disordered potential which exhibits interesting diffusive behavior.

4 pages, 4 figures. Comments welcome

References in corpus (4)

• Exact relaxation in a class of non-equilibrium quantum lattice systems
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• The Amplitude Mode in the Quantum Phase Model
• Classical Diffusion of a quantum particle in a noisy environment

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