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Universal spreading of wave packets in disordered nonlinear systems.
S Flach1, D O Krimer, Ch Skokos
1Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
Physical Review Letters
|March 5, 2009
Summary
Nonlinearity causes initially localized wave packets to spread in disordered chains, leading to transient localization or immediate subdiffusion. This spreading, driven by weak chaos, results in the packet
Area of Science:
- Condensed Matter Physics
- Nonlinear Dynamics
- Wave Propagation in Disordered Media
Background:
- In disordered systems, eigenmodes typically exhibit Anderson localization, confining waves spatially.
- Nonlinearity can alter wave packet dynamics, potentially overcoming localization effects.
Purpose of the Study:
- To investigate the impact of nonlinearity on the spatial spreading of wave packets in disordered chains.
- To characterize the different evolution outcomes and the underlying mechanisms of wave packet spreading.
Main Methods:
- Analysis of wave packet dynamics in a disordered chain model incorporating nonlinearity.
- Identification of frequency shifts induced by nonlinearity as key factors in evolution outcomes.
- Characterization of subdiffusive spreading and its dependence on disorder strength.
Main Results:
- Nonlinearity leads to three distinct wave packet evolution outcomes: transient localization followed by subdiffusion, immediate subdiffusion, or self-trapping with partial subdiffusion.
- Subdiffusive spreading is attributed to a finite number of resonant packet modes, independent of time on average.
- The second moment of the wave packet grows as t^(1/3), indicating anomalous subdiffusion.
Conclusions:
- Nonlinearity fundamentally changes wave packet behavior in disordered systems, transitioning from localization to spreading.
- Weak chaos within the packet drives the slow, subdiffusive spreading by interacting with resonant modes.
- The observed subdiffusion exponent (alpha=1/3) provides a quantitative measure of anomalous transport in this nonlinear disordered system.
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