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Anderson localization or nonlinear waves: a matter of probability
M V Ivanchenko1, T V Laptyeva, S Flach
1Theory of Oscillations Department, University of Nizhniy Novgorod, Nizhniy Novgorod, Russia.
Anderson localization in nonlinear disordered systems is probabilistic. A finite nonlinearity allows wave packets to propagate, with this probability increasing with energy and reaching one at a threshold dependent on wave packet size.
Area of Science:
- Condensed matter physics
- Wave phenomena in disordered media
Background:
- Anderson localization describes wave packet confinement in linear disordered systems.
- The behavior of wave packets in nonlinear disordered systems remains a subject of theoretical and experimental debate.
Purpose of the Study:
- To resolve the dispute regarding wave packet behavior (localization vs. propagation) in nonlinear disordered systems.
- To investigate the probabilistic nature of Anderson localization breakdown.
Main Methods:
- Theoretical analysis of wave packet dynamics in nonlinear disordered systems.
- Investigation of the influence of nonlinearity (energy) and wave packet size on localization.
Main Results:
- Anderson localization is not absolute in nonlinear disordered systems; it has a probabilistic outcome.
- A finite nonlinearity (energy) introduces a non-zero probability for wave packet propagation.
- This propagation probability increases with nonlinearity and depends on the initial wave packet size, reaching unity at a threshold.
- The spreading probability remains finite even for infinite packet sizes at fixed energy, generalizing to higher dimensions.
Conclusions:
- The fate of wave packets in nonlinear disordered systems is probabilistic, not exclusive.
- Nonlinearity and energy play crucial roles in overcoming Anderson localization.
- Findings offer a generalized understanding of wave propagation in complex media.
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