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Destruction of Anderson localization by a weak nonlinearity
A S Pikovsky1, D L Shepelyansky
1Department of Physics, University of Potsdam, Am Neuen Palais 10, D-14469, Potsdam, Germany.
Physical Review Letters
|March 21, 2008
Summary
Nonlinearity can destroy Anderson localization in disordered lattices, leading to unlimited wave packet spreading. Above a critical nonlinearity, subdiffusive spreading occurs, unlike the localized behavior seen with small nonlinearities.
Area of Science:
- Quantum physics
- Condensed matter physics
- Nonlinear dynamics
Background:
- Anderson localization describes the suppression of diffusion in disordered systems.
- Disordered nonlinear systems exhibit complex behaviors not fully understood.
- Wave packet spreading in lattices is crucial for transport phenomena.
Purpose of the Study:
- To investigate the effect of nonlinearity on Anderson localization in disordered lattices.
- To determine the conditions under which wave packet spreading occurs.
- To characterize the nature of this spreading (e.g., subdiffusive).
Main Methods:
- Numerical simulations of a one-dimensional discrete nonlinear Schrödinger lattice.
- Introduction of disorder into the lattice.
- Analysis of wave packet spreading using the second moment.
Main Results:
- Above a critical nonlinearity, Anderson localization is destroyed.
- Unlimited subdiffusive spreading of the wave packet is observed.
- The second moment grows as t^alpha, with alpha between 0.3-0.4.
- For small nonlinearities, wave packets remain localized.
Conclusions:
- Nonlinearity is key to overcoming Anderson localization in disordered systems.
- Subdiffusive spreading is a distinct transport regime in these nonlinear disordered lattices.
- The findings have implications for understanding wave propagation in complex media.
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