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Spreading of wave packets in disordered systems with tunable nonlinearity
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
We investigated excitation spreading in disordered Klein-Gordon chains. Subdiffusive spreading was observed, with results matching theoretical predictions for various nonlinearities and dephasing conditions.
Area of Science:
- Condensed matter physics
- Nonlinear dynamics
- Disordered systems
Background:
- Single-site excitations in disordered systems exhibit complex dynamics.
- The Klein-Gordon equation describes systems with both nonlinearity and disorder.
- Anderson localization is a key phenomenon in disordered media.
Purpose of the Study:
- To investigate the spreading of single-site excitations in 1D disordered Klein-Gordon chains.
- To explore the effect of tunable nonlinearity, |u(l)|(σ)u(l), on excitation spreading.
- To analyze the influence of dephasing on wave packet dynamics.
Main Methods:
- Extensive numerical simulations of wave packet evolution.
- Analysis of wave packet spreading using the second moment growth (tα).
- Comparison of numerical results with theoretical predictions for varying nonlinearity (σ).
Main Results:
- Observed subdiffusive spreading of wave packets, characterized by tα.
- Numerical results for the exponent α showed excellent agreement with theoretical predictions.
- Dephasing was included in simulations, with agreement for σ≥2.
- Evidence of strong chaos and destruction of Anderson localization at small σ was found.
Conclusions:
- The study provides a comprehensive understanding of excitation spreading in disordered nonlinear systems.
- Theoretical predictions for subdiffusive spreading are validated across different nonlinearity strengths and dephasing conditions.
- The findings highlight the interplay between nonlinearity, disorder, and dephasing in determining wave packet dynamics.
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