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Published on: July 29, 2013
Localization-delocalization transition and subdiffusion of discrete nonlinear Schrödinger equation in three
1Department of Mathematical and Design Engineering, Gifu University, Gifu 501-1193, Japan.
Summary
Nonlinearity in the discrete nonlinear Schrödinger equation (DNLSE) promotes wave delocalization in 3D systems. Subdiffusive wave packet spreading is observed, with exponents varying based on system properties.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Nonlinear Dynamics
Background:
- Understanding wave localization and delocalization is crucial in disordered systems.
- The discrete nonlinear Schrödinger equation (DNLSE) models various physical phenomena, including wave propagation in disordered media.
Purpose of the Study:
- To investigate the localization-delocalization transition in a 3D DNLSE with random potentials.
- To numerically clarify the influence of nonlinearity on wave localization phenomena.
- To analyze wave packet spreading and subdiffusive behavior in this system.
Main Methods:
- Numerical simulations of the 3D DNLSE with random potentials.
- Thouless-number analysis to quantify localization.
- Wave packet spreading analysis to observe transport dynamics.
Main Results:
- Nonlinearity was found to promote the delocalization of stationary states in the 3D DNLSE.
- Subdiffusive wave packet spreading was observed in the 3D system under strong nonlinearity.
- In a 1D DNLSE with correlated disorder, the subdiffusion exponent was found to be non-universal.
Conclusions:
- Nonlinearity plays a key role in overcoming Anderson localization in 3D disordered systems.
- The observed subdiffusion indicates anomalous transport properties in the nonlinear regime.
- The non-universality of subdiffusion exponents highlights the importance of specific system parameters in DNLSE.
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